Question

The square root of a product of two positive real numbers is the product of their square roots. Write an algebraic expression based on that statement.

Answer 1

Explanation:

• The square root of a product of two positive real numbers is the product of their square roots.

Let 4 and 5 be the two positive real number. The square root of a product of 4 and 5 is the product of their square roots.

`√(4\cdot 5)`

`=√(20)`

`=√(2^2\cdot \:5)`

`\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}`

`=√(5)√(2^2)`

so

`=√(5)√(2^2)`

`\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a`

`√(2^2)=2`

Therefore,

`√(4\cdot \:5)=2√(5)`

NOW SOLVING BY APPLYING RADICAL RULE such that

`\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}`

`√(4\cdot 5)=√(4)√(5)`

as

`√(2^2)=2`

so

`=2√(5)`

Hence, The square root of a product of two positive real numbers is the product of their square roots.