Question

rationalize the denominator 1/root 7
$rationalise denominator 1 \ \sqrt{?} 7$
​

Answer 1

Given:

• A number is $\dfrac{1}{\sqrt7}$

To Find:

• Rationalize the number

Solution:

As we know we have to multiple denominator its numerator and denominator by its rationalising factor.So let's do

$\: \: \sf \: \frac{1}{ \sqrt{7} } \times \frac{ \sqrt{7} }{ \sqrt{7} }$

Now Multiple the numbers

$\: \: \: \sf \: \frac{ \sqrt{7} }{ \sqrt{( {7})^{2} } }$

Now split the denominator

$\: \: \sf \: \frac{ \sqrt{7} }{ \sqrt{7 \times \sqrt{7} } }$

And as we know when two same square root number is multiply then we get that same digit

$\: \: \sf \: \frac{ \sqrt{7} }{7}$

Hence, √7/7 is the rationalize number.

Additional Information:

• If the product of two irrational numbers is rational then each one is called the rationalising factor of the other.