How do you evaluate #\sqrt { 2^ { 6} \cdot 7^ { 4} }#?

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Answer 1 · 2016-12-23T19:23:50

#sqrt(2^6xx7^4)=392#

If we have a square root #sqrt(2xx3)#, we can split it into each multiplicand so we get #sqrt(2)xxsqrt(3)#.

Using this principle in the above case, we can rewrite the equation in this form:

#sqrt(2^6xx7^4)=sqrt(2^6)xxsqrt(7^4)#

We can rewrite the square roots by raising the numbers to the power of #1/2#

#sqrt(2^6)xxsqrt(7^4)=(2^6)^(1/2)xx(7^4)^(1/2)#

Simplifying this, we get:

#(2^6)^(1/2)xx(7^4)^(1/2)=2^3xx7^2#

Now that we have the exponents in positive integer form, we can easily solve the equation:

#2^3xx7^2=8xx49=392#