what is square root of 17a^2?

ACTUALLY 17 a^2 means 17 x a^2 therefore square root of 17 a^2 = a x root 17

or = a x 4.123105.........

The plus or minus answer are wrong, as are the a*√17 answers. First, note that 17a² is 17 times (a²). Order of operations puts the "a to the second power" operation ahead of the "multiply by 17" operation. So, using the product power of square roots:

√(17a²) = √17 * √(a²)

Here's the detail that everyone had missed, when I started typing anyway: √(a²) = |a|

There are two possible square roots for a positive number, but the √ symbol specifically means the POSITIVE square root. So, if a is a negative number, a² will be a positive number, and √(a²) will also be positive. That's where the absolute value bars come from. So the a√17 answer only works if a is 0 or positive.

Edit: Fixed a typo, and the final answer is |a|*√17 .... or (√17) |a| if you like the number first, even if it is under a radical.

If the 17 and the a^2 are both under the radical, then it is the square root of 17, times the absolute value of a, which would be written as |a|√17

If the a^2 is outside the radical, then it is simply a^2 √17

If you are wondering how to treat

17a^2

It is 17, times the square of a. Only if the 17a is inside parentheses, with the exponent outside them -- written as (17a)^2 -- that you would square the 17. And, if you had that, then your answer would become |17a|

The total quantity that is asked to make a square root is indicated either by a LINE BRACKET over the entire area or by using a 1st or 2nd or 3rd bracket that begins just after the root sign.

IN YOUR CASE square root should save been followed by a bracket as : square root of(17a^2) =? to get the answer =4.123 a

But absence of bracket after the square root makes it=(square root of 17)*a^2 =4.123.a^2

In general, √(ab) = (√a)(√b). So applying the same thing here gives you (√17)(a), which is a√17.

That's the exact answer. There's absolutely no need to write out √17 as some crappy rounded-off decimal.

Some other people are saying ±a√17, but that's incorrect. When you have a radical to begin with, it's assumed that you take only the positive square root.

square root of 17a^2 = a times (sqrt17) = a(sqrt17) = 4.123a

Similar problem: sqrt of (36) = sqrt( 4 times 9) = 2sqrt(9) = 2 times 3 = 6

The square root of that total would be a*sqrt(17) because the 17 is under the square root as well.

Well, if you have sqrt(m*n) where m and n are two quantities, that is equal to sqrt(m)*sqrt(n). In this case, that means sqrt(17a^2)=sqrt(a^2)*sqrt(17)=a*sqrt(17).

More proof that parentheses are our friends :)

And I agree the answer is plus or minus a times the sqr root of 17

calculator

sqrt17*a = 4.1231056..............................................*a