Question

rationalise the denominator and simplify 5√3+√2/√3+√2

Answer 1

Answer:

Mark this as brain list answer

Step-by-step explanation:

5√3+√2/√3+√2

5√2+√2/√3+√2×√3-√2/√3-√2

(√3-√2)(5√3+√2)/3-2

15+√6-5√6-2/1

15-4√6-2

=15-4√6-2

Answer 2

Answer:

After rationalisation required answer is (13-4√6)

Step-by-step explanation:

Given,

$\frac{5 \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} }$

We want to rationalise the denominator

Here denominator of

$\frac{5 \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} }$

is (√3+√2) and numerator of

$\frac{5 \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} }$

is (5√3+√2)

We are multiplying denominator and numerator of

$\frac{5 \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} }$

by (√3-√2)

So,

$\frac{(5 \sqrt{3} + \sqrt{2} )( \sqrt{3} - \sqrt{2}) }{ \sqrt{3} + \sqrt{2} ( \sqrt{3} - \sqrt{2}) } \\ = \frac{5 \times 3 - 5 \sqrt{6} + \sqrt{6} - 2 }{ {( \sqrt{3} )}^{2} - ( { \sqrt{2}) }^{2} } \\ = \frac{15 - 4 \sqrt{6} - 2}{3 - 2} \\ = \frac{13 - 4 \sqrt{6} }{1} \\ = 13 - 4 \sqrt{6}$

Here applied formulas are

${x}^{2} - {y}^{2} = (x + y)(x - y) \\ \sqrt{x} \times \sqrt{y} = \sqrt{xy} \\ \sqrt{x} \times \sqrt{x} = x$

This is a problem of power of indices.

Some important formulas of Power of indices :

${x}^{0} = 1 \\ {x}^{1} = x \\ {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{ {y}^{a} } = {x}^{ya} \\ {x}^{ - 1} = \frac{1}{x} \\ {x}^{a} \times {y}^{a} = {(xy)}^{a}$

Know more about Power of indices,

1.https://brainly.in/question/21620304

2.https://brainly.in/question/10752814

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