simplify square roots?

Question

√45x^2

√45x^3

√90x^2y^3

Answer 1

√45x^2

This is the same as

√9 * 5 * x^2
3√5x^2

Since the x is squared, you can take the square root of it, which is just x.

3x√5


√45x^3
√9 * 5 * x^2 * x
3x√5x

√9 * 10 * x^2 * y^2 * y

3xy√10y

Get it? IM me if you need a more detailed description.

Answer 2

If you factor the 45 and the 90, that will be a good start. In the first one, 45 = 3x3x5, so you can take a 3 and an x out. The answer would be /5 times 3x.

In the second one, there would be one x still under the root sign, so it would be /5x times 3x.

In the third one, 90 factors to 2x3x3x5. You can take a 3 out, an x, and a y. There's still one y under the root sign. So the answer would be /10y times 3xy.

My "/" is a root sign. Hope that helps.

Answer 3

√(45x²) = 3|x|√5

√x² = |x|, not x, since √(-3)² = √9 = 3 <> -3

√(45x^3) = 3|x|√(5x)

√(90x²y^3) = 3|xy|√(10y)

Answer 4

√(45x²)
√(9*5x²)
±3x√5


√(45x^3)
√(9 * 5 * x² * x)
±3x√(5x)


√(90x²y^3)
√(9 * 10 * x² * y² * y)
±3xy√(10y)

Answer 5

The first has the square factor 9x^2 inside the radical. take that square root and you have 3x*sqrt(5)

The second has the exact same square factor, but this time you're left with 5x inside. 3x*sqrt(5x)

The third and last has the square factor 9x^2y^2 so take that out as 3xy and you have 3xy*sqrt(10y)

Answer 6

First one = 45x

Answer 7

3x sqrtof 5
3x sqrt of 5x
3xy sqrt of 10y

Answer 8

the square root of a number is that number times itself

Answer 9

3xsqrt(5)
3xsqrt(5x)
3xysqrt(y)