simplify √90 x^4?

Question

would the answer be 3 x^2 √10 or 3 x√10x

im confused because exponents are multiplied and the square root is for the base number right??

Answer 1

It's the first.
√90 x^4 = √9 * 10 * x^2 * x^2
therefore,
√90 x^4 = 3 x^2 √10

Answer 2

It takes two square roots multiplied together to get you a whole number. For instance, sqrt of 3 times sqrt of 3 is 3.

In your problem, break down the sqrt of 90 first into its primes. Those are sqrt 3, sqrt 3, sqrt 2 and sqrt 5. You have two sqrt 3's, so that part becomes integer 3. There are not two sqrt 2's nor two sqrt 5's, so recombine them into sqrt 10. You have now got 3 sqrt 10.

For the x's you have four. Remembering it takes two to get a whole number, the first two sqrt x's give an x. The next two x's give another whole number x. There is no reminder to remain under the sqrt like, like there was with the 10 previously. Thus, the letter part of your problem becomes x^2.

Final answer: 3x^2 sqrt 10.

Answer 3

3 x^2 √10

Answer 4

As you have entered it now, square root applies to 90 alone!

In "square root (90 x^4)" said square root is applicable to both 90 and x^4 (as both are 'within a bracket')!

Obviously that is what you wanted, which can be made out from one of your correct answers 3 x^2*sq.rt 10.

This confusion is quite usual!

Regards!

Answer 5

sqr=square root
if the problem is: sqr(90x^4) then:
90=2*5*3*3 (primes factors)
sqr(90x^4)=sqr(2*5*3^2*x^4)
remember: sqr(x^a)=x^(a/2) then:
[(3^2)^1/2]*[(x^4)^1/2]*sqr(2*5)
simplifying:
3*x^2*sqr(10)

Answer 6

yes your correct, the base needs to be multiplyef by the area squAred/

Answer 7

3x^2 * (sqrt 10)