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.
[tex]\sqrt{4\cdot 5}[/tex]
[tex]=\sqrt{20}[/tex]
[tex]=\sqrt{2^2\cdot \:5}[/tex]
[tex]\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}[/tex]
[tex]=\sqrt{5}\sqrt{2^2}[/tex]
so
[tex]=\sqrt{5}\sqrt{2^2}[/tex]
[tex]\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a[/tex]
[tex]\sqrt{2^2}=2[/tex]
Therefore,
[tex]\sqrt{4\cdot \:5}=2\sqrt{5}[/tex]
NOW SOLVING BY APPLYING RADICAL RULE such that
[tex]\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}[/tex]
[tex]\sqrt{4\cdot 5}=\sqrt{4}\sqrt{5}[/tex]
as
[tex]\sqrt{2^2}=2[/tex]
so
[tex]=2\sqrt{5}[/tex]
Hence, The square root of a product of two positive real numbers is the product of their square roots.
