Question

Simplify : 7 to the power 1/2 multiplied by 8 to the power 1/2

Answer 1

( 7)^(1/2) × 8^(1/2)

What we do in such cases is we just simply multiply the base and keep the power same .

So it becomes

56^(1/2)

Answer 2

The simplified form of the expression $7^{\frac{1}{2} }*8^{\frac{1}{2} }$ is $2\sqrt{14}$.

Given,

An expression:  $7^{\frac{1}{2} }*8^{\frac{1}{2} }$.

To Find,

The simplified form of the given expression.

Solution,

The method of finding the simplified form of the given expression is as follows -

We know by the rules of exponents $a^{m}*b^{m}=(ab)^{m}$, where a,b, and m are three real numbers.

Applying this rule in the given expression,

$7^{\frac{1}{2} }*8^{\frac{1}{2} }= (7*8)^{\frac{1}{2} }=(4*14)^{\frac{1}{2} }$

$=4^{\frac{1}{2} }*14^{\frac{1}{2} }=2*14^{\frac{1}{2} }=2\sqrt{14}$$2\sqrt{14}$.

Hence, the simplified form of the expression $7^{\frac{1}{2} }*8^{\frac{1}{2} }$ is $2\sqrt{14}$.

#SPJ3