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

Step-by-step 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.

$\sqrt{4\cdot 5}$

$=\sqrt{20}$

$=\sqrt{2^2\cdot \:5}$

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

$=\sqrt{5}\sqrt{2^2}$

so

$=\sqrt{5}\sqrt{2^2}$

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

$\sqrt{2^2}=2$

Therefore,

$\sqrt{4\cdot \:5}=2\sqrt{5}$

NOW SOLVING BY APPLYING RADICAL RULE such that

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

$\sqrt{4\cdot 5}=\sqrt{4}\sqrt{5}$

as

$\sqrt{2^2}=2$

so

     $=2\sqrt{5}$            

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