Find the value of the following correct to three places of decimals- it being given that- -2-1-4142- -3-1-732- -5 - 2-236- -6-2-4495 and -10 - 3-162ii 1- -23 - 2-2

Name: RDSHA - Garde 09 - Mathematics - Rationalisation - Q12_2
Uploaded: 2022-07-04T10:36:42+05:30
Description: Given: 1 + √(2)3 − 2√(2) Rationalising the denominator, =(1+√(2))(3+2√(2))(3 − 2√(2))(3+2√(2)) =3+2√(2)+3√(2)+43^2−(2√(2))^2 ( using identity, a^2−b^2= (a−b ...

Given: 1 + √(2)3 − 2√(2) Rationalising the denominator, =(1+√(2))(3+2√(2))(3 − 2√(2))(3+2√(2)) =3+2√(2)+3√(2)+43^2−(2√(2))^2 ( using identity, a^2−b^2= (a−b ...

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Question

Find the value of the following correct to three places of decimals, it being given that, $\sqrt{2} = 1.4142, \sqrt{3} = 1.732, \sqrt{5} = 2.236, \sqrt{6} = 2.4495$ and $\sqrt{10} = 3.162$

(ii) $\frac{1 + \sqrt{2}}{3 - 2 \sqrt{2}}$

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Solution

Given: $\frac{1 + \sqrt{2}}{3 - 2 \sqrt{2}}$

Rationalising the denominator,

$= \frac{(1 + \sqrt{2}) (3 + 2 \sqrt{2})}{(3 - 2 \sqrt{2}) (3 + 2 \sqrt{2})}$

$= \frac{3 + 2 \sqrt{2} + 3 \sqrt{2} + 4}{3^{2} - (2 \sqrt{2})^{2}}$

( using identity, $a^{2} - b^{2} = (a - b) (a + b)$ )

$= \frac{7 + 5 \sqrt{2}}{9 - 8}$

$= \frac{7 + 5 \sqrt{2}}{1}$

$= 7 + 5 \sqrt{2}$

$= 7 + 5 \times 1.4142$

$= 7 + 7.071$

$= 14.071$

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Find the values of each of the following correct to three places of decimals, it being given that $\sqrt{2} = 1.4142, \sqrt{3} = 1.732, \sqrt{5} = 2.2360, \sqrt{6} = 2.4492 a n d \sqrt{10} = 3.162$ .