Question

Using complete sentences, explain the two ways to simplify sqrt 147 and provide the simplified form.

Answer 1

sqrt(x) is the same as x^(1/2) It is an exponent therefore you can use rules and properties of exponents.

147 can be factored to 7^2 and 3 therefore

(7^2 * 3) ^ (1/2) = (7^2)^(1/2) * 3^(1/2)= 7 * sqrt (3)


if you look at the 7's exponent it is this (1/2+2)=1 there fore 7^1 is 7.