Question

What is 1/root 2 into 1/root 2

Answer 1

QUESTION :-

1/√2 × 1/√2

ANSWER :-

1/2

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Answer 2

Answer:

The value of $\frac{1}{\sqrt{2} }$ ×$\frac{1}{\sqrt{2} }$ = $\frac{1}{2}$

Step-by-step explanation:

Required to find

$\frac{1}{\sqrt{2} }$ ×$\frac{1}{\sqrt{2} }$

Recall the formula

For any number 'a'

√a ×√a = (√a)² = a

Solution

Here √2 is an irrational number and  $\frac{1}{\sqrt{2} }$ is also an irrational number.

Irrational numbers are the numbers that cannot be expressed in the form $\frac{p}{q}$

In order to multiply the given two irrational numbers, we have

$\frac{1}{\sqrt{2} }$ ×$\frac{1}{\sqrt{2} }$ = $\frac{1}{\sqrt{2}X\sqrt{2} }$

Since √2 ×√2 = (√2)² = 2, we have

$\frac{1}{\sqrt{2} }$ ×$\frac{1}{\sqrt{2} }$ = $\frac{1}{2}$

∴ The value of $\frac{1}{\sqrt{2} }$ ×$\frac{1}{\sqrt{2} }$ = $\frac{1}{2}$

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