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### Formative Assessment_MCQ

**Question No. 4**

We know that rationalization factor for is. Hence rationalization factor of is.Hence correct option is

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### Formative Assessment_MCQ

**Question No. 5**

Given that.Hence is given as

.We need to find

We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Therefore,

Hence the correct option is.

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### Formative Assessment_MCQ

**Question No. 6**

Given that:

We are asked to find *a* and *b*

We know that rationalization factor for is . We will multiply numerator and denominator of the given expression by, to get

On equating rational and irrational terms, we get

Comparing rational and irrational part we get

Hence, the correct choice is.

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### Formative Assessment_MCQ

**Question No. 7**

Given that:.To find simplest rationalizing factor of the given expression we will factorize it as

The rationalizing factor of is, since when we multiply given expression with this factor we get rid of irrational term.

Therefore, rationalizing factor of the given expression is

Hence correct option is.

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### Formative Assessment_MCQ

**Question No. 8**

We know that rationalization factor for is. Hence rationalization factor of is.

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### Formative Assessment_MCQ

**Question No. 9**

We know that rationalization factor for is. Hence rationalization factor of is.

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### Formative Assessment_MCQ

**Question No. 10**

Given that:

We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Therefore,

On squaring both sides, we get

Hence the value of the given expression is.

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### Formative Assessment_MCQ

**Question No. 11**

Given that,

Hence is given as

We need to find

We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Since so we have

Therefore,

Hence the value of the given expression is.

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### Formative Assessment_MCQ

**Question No. 12**

Given that .It can be simplified as

We need to find

Therefore,

Hence the value of the given expression is 8.Hence correct option is .

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### Formative Assessment_MCQ

**Question No. 13**

Given that .It can be simplified as

Therefore,

Hence the value of the given expression is.

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### Formative Assessment_MCQ

**Question No. 14**

Given that and.

We are asked to find

Now we will rationalize *x*. We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Similarly, we can rationalize *y*. We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Therefore,

Hence the value of the given expression is.

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### Formative Assessment_MCQ

**Question No. 15**

Given that and.

We need to find

Now we will rationalize *x*. We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Similarly, we can rationalize *y*. We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Therefore,

Hence the value of the given expression is.

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### Formative Assessment_MCQ

**Question No. 16**

Given that:.It can be written in the form as

Hence the value of the given expression is.

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### Formative Assessment_MCQ

**Question No. 17**

Given that:.It can be written in the form as

Hence the value of the given expression is.

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### Formative Assessment_MCQ

**Question No. 18**

Given that , we need to find the value of .

We can rationalize the denominator of the given expression. We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Hence the value of the given expression is 0.14142 and correct choice is.

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### Formative Assessment_MCQ

**Question No. 19**

We can factor out from the given expression, to get

Hence the value of expression must closely resemble be

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### Formative Assessment_MCQ

**Question No. 20**

Given that:.To find square root of the given expression we need to rewrite the expression in the form

Hence the square root of the given expression is

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### Formative Assessment_MCQ

**Question No. 21**

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### Formative Assessment_MCQ

**Question No. 22**

We can factor irrational terms as

Hence the value of given expression is.

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### Formative Assessment_MCQ

**Question No. 23**

Hence the value of the given expression is 20 and correct option is.

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### Formative Assessment_MCQ

**Question No. 24**

We need to find *a*

The given expression can be simplified by taking square on both sides

The irrational terms on right side can be factorized such that it of the same form as left side terms.

Hence,

On comparing rational and irrational terms, we get.Therefore, correct choice is .

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### Formative Assessment_MCQ

**Question No. 25**

Given that: .We need to find *x* and *y*

We know that rationalization factor for is . We will multiply numerator and denominator of the given expression by, to get

On equating rational and irrational terms, we get

### Page No. 32

### Exercise : 3.1

**Question No. 1**

(i) We know that. We will use this property to simplify the expression.

Hence the value of the given expression is .

(ii) We know that. We will use this property to simplify the expression.

Hence the value of the given expression is.

### Page No. 32

### Exercise : 3.1

**Question No. 2**

(i) We can simplify the expression as

Hence the value of the expression is

(ii) We can simplify the expression as

Hence the value of the expression is

(iii) We can simplify the expression as

Hence the value of the expression is .

### Page No. 32

### Exercise : 3.1

**Question No. 3**

(i) We know that. We will use this property to simplify the expression.

Hence the value of expression is 110.

(ii) We know that. We will use this property to simplify the expression.

Hence the value of expression is 18.

(iii) We know that. We will use this property to simplify the expression.

Hence the value of expression is 6

(iv) We know that. We will use this property to simplify the expression.

Hence the value of expression is 6.

(v) We know that. We will use this property to simplify the expression.

Hence the value of expression is 3.

### Page No. 33

### Exercise : 3.1

**Question No. 4**

(i) We know that. We will use this property to simplify the expression.

Hence the value of expression is

(ii) We know that. We will use this property to simplify the expression.

Hence the value of expression is

(iii) We know that. We will use this property to simplify the expression.

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