how do i get to the square root of sqrt15*sqrt35 if the answer is 5sqrt21?

Question

what is the easiet way to do this problem and always get it right?

Answer 1

OK!

Factor both numbers and group like terms:

sqrt15*sqrt35 = sqrt (15*35) = sqrt (3 * 5 * 5 * 7)

= sqrt (5^2 * 3 * 7) = 5 * sqrt (3*7) = 5sqrt21

Done!

Answer 2

you can multiply the numbers inside the square root
(remember that they BOTH have to be square roots)

square root of 5 * cube root of 6 cannot be multiplied because they have different n-roots., one is cube and the other is square.

cube root of 6 * cube root of 5 is equal to cube root of 30., (because they are both cube roots, they are raised to the same power of 1/3, just as square roots are raised to the power of 1/2. and numbers with different base but same exponents can be multiplied and divided, like 2^2 * 3^2 = 6^2., only with square roots the numbers are raised to 1/2 -a fraction)

so sqrt15 * sqrt35 is the same as [ sqrt (15 * 35) ]

there are two ways to do this,

you can factor out 15 and 35 first

so you'd get (5 * 3) * (5 * 7)

you can now bring out 5 (since they occur twice and you're looking for a sqare root, if you're looking for a cube root, a number must appear thrice before you can bring it out.)

and simplify 3*7 since they are no longer factorable

so you'd get 5 and sqrt of 21., done

this is the faster.,

the other way is to multiply 15 and 35 first then get its factor, which would be a larger number and larger numbers are harder to factor out, so stick with the first one.,

Answer 3

square root of sqrt15*sqrt35
1. Rationalize the roots
(sqrt of sqrt15xsqrt35)² = (x)²
2. Cut the root
sqrt15xsqrt35 = x
Calculate: sqrt15*35 = \/525 =>
\/525| 3
..175| 5
....35| 5
..... 7| 7
;;;;;;1
\/525 = \/(3. 5.5.7) = \/3.\/5².\/7 = 5\/21.
>><

Answer 4

√15 * √35=√15*35=√525=√25*21=5√21

Answer 5

sqrt15*sqrt35=sqrt(15*35)
then take the sqrt. of that.
you get sqrt(5sqrt21)
unless you are wrong in math and did not write the answer clearly, you are wrong.

Answer 6

so first when you multiply square roots....you just multiply what is under them together...so you have sqrt(15*35) or sqrt(525) ...then you have to reduce it. Since the largest perfect square that goes into 525 is 25.......you can take that out....and when you take out sqrt25...you just have 5. and 525/25 is 21 so you are left with that under the sqrt sign.

Answer 7

sqrt15*sqrt35
= sqrt(15*35)
=sqrt(3*5*7*5)
=sqrt(5*5)*sqrt(7*3)
=5sqrt(21)

Answer 8

sqrt(15) * sqrt(35) = sqrt(15 * 35) = sqrt(25 * 21) = 5sqrt(21)

to help you understand how i got sqrt(15 * 35), i just took it like this in my head sqrt(5 * 3 * 5 * 7) = sqrt(5 * 5 * 3 * 7) = sqrt(25 * 21)

Answer 9

Since these squareroots are decimals, the best hing is to do it on the calculator
sqrt(sqrt(15)*sqrt(35))
Then check to see if this is the same decimal as
5*sqrt(21)
It is not.

Answer 10

=sqrt(15*35)
=sqrt(5*3*7*5)
=5sqrt21