Rewrite the following in simplified radical form.?

Question

(square root) (45 x^8)

Assume that all variables represent positive real numbers.

Answer 1

√(45 x^8)
= √(5×9×x^8)
= √5 × √9 × √x^8
= √5 × 3 × x^4
= (3√5)x^4.

Answer 2

In simplifying, the idea is to get everything out from under the radical sign that you can. Because the power of x is divisible by 2, you can therefore divide the power by 2 and pull the term in x out from under the radical sign entirely. You can also break up the coefficient 45 into 9 * 5, 9 being the perfect square of 3, and pull the 3 out. You can't do anything with the remaining factor 5 except leave it under the radical sign, which is what you do. The answer is therefore

3√5 * x^4

If x had been taken to an odd power - which was not the case here - you could break the x up into the largest even power, times the odd x. You could then take the square root of the even power of x by dividing the power by 2 and leave the odd x under the radical sign.

Answer 3

sqrt ( 45^8 ) = (45^8)^0.5 = 45^4

Answer 4

3x^4sqruare root(5)

Answer 5

sqrt(45x^8)=(sqrt9)((sqrt5)x^4
=3(sqrt5)x^4, =3x^4(sqrt5)