Question

How can we say that 30/ root3 =10 root3

Answer 1

To prove : 30/√3 = 10√3

30/√3 =3*10/√3

=√3 * √3 * 10/√3

=10 * √3

Hence Proved

Answer 2

Concept:

The square root of a number is the inverse procedure of squaring a number. A number's square root is the number that, when multiplied by itself, returns the original number.

Given:

The given equation is $\frac{30}{\sqrt{3} }=10\sqrt{3}$ .

Prove:

To prove the given equation.

Solution:

Multiply the left-hand side of the given equation by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$=\frac{30}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}}$

$=\frac{30\sqrt{3}}{\sqrt{3}*\sqrt{3}}$

$=\frac{30\sqrt{3}}{3}$   (∵ $\sqrt{3} *\sqrt{3} =3$)

$=10\sqrt{3}$

which is equal to the right-hand side of the equation.

∴  $\frac{30}{\sqrt{3} }=10\sqrt{3}.$

Hence proved.