Test: Square Roots - SAT MCQ

The square root of 169 is 13
because 13 x 13 = 169.

256 is a perfect square because √256 = 16, and 16 x 16 = 256.

√(36x²) = √(6x x 6x) = 6x

If √x = 7,
then
x = 7 x 7 = 49.

If y = √(81x²) and x = 3,
then y = √(81 x 3²) = √(81 x 9) = √729 = 9 x 3 = 27.

The square root of 196 is a positive number, so we can eliminate options b) and d). 
The square root of 196 is 14, as 14 x 14 = 196.

√(100x²)
= √(10x x 10x)
= 10x

If √(x² - 6x) = 4, we can square both sides to get x² - 6x = 16.
Solving for x, we get x² - 6x - 16 = 0.
Factoring,
we find (x - 8)(x + 2) = 0,
so x = 8,-2.

If 2√a = 8, we can first divide both sides by 2 to get √a = 4.
Squaring both sides, we find a = 16.

We can simplify 1/9 to √(1/3)².
Then, we can take the square root of both sides: √(1/9) = 1/3.
Therefore, the answer is a) 1/3.