Question

Rationalize the denominator of: 1 3√2+4​

Answer 1

Answer:

(3√2 - 4)/2

Step-by-step explanation:

1/(3√2 + 4)

⇒ [1 × (3√2 - 4)] / (3√2+4)(3√2 - 4)

⇒(3√2 - 4) / ((3√2)²  -   4²)

⇒(3√2 - 4) / ( 18 - 16 )

⇒(3√2 - 4) / (2)

Answer 2

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■ GIVEN THAT:-

$\frac{1}{3 \sqrt{2} + 4}$

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■ SOLUTION:-

we can get the solution by Multiplying both numerator and denominator with 3 square root 2 minus 4.

$\frac{1}{3 \sqrt{2} + 4 } = \frac{1}{3 \sqrt{2} + 4} \times \frac{3 \sqrt{2} - 4}{3 \sqrt{2} - 4}$

Now, In denominator we used the identity

$(x + y)(x - y) = {x}^{2} - y ^{2}$

We get,

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

$= \frac{3 \sqrt{2} - 4}{18 - 16} = \frac{3 \sqrt{2} - 4}{2}$

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Hope it helps you

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