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Serga [27]
3 years ago
12

The square root of a product of two positive real numbers is the product of their square roots. Write an algebraic expression ba

sed on that statement.
Mathematics
1 answer:
Sliva [168]3 years ago
5 0

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.

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