Question

Quick

Which statements about square roots are true? Check all that apply.
O The square root of a positive number cannot be negative.
O All positive numbers have two square roots.
O√189 because 9(2) = 18.
O √49 = 7 because 7(7) = 49.
O √25 = 5 because 5²= 25.

Answer 1

B, D, E

Explanation:

You want to know which of these statements about square roots are true:

(a) The square root of a positive number cannot be negative.

(b) All positive numbers have two square roots.

(c) √18 = 9 because 9(2) = 18

(d) √49 = 7 because 7(7) = 49

(e) √25 = 5 because 5² = 25

Square root

The square root of a number is a number that multiplies itself to give the original number:

√a = x ⇒ x·x = x² = a

If x is a square root of 'a', then -x is also a square root of 'a':

(-x)² = x² = a

So, all positive numbers have two square roots, choice B.

One of those square roots is negative: eliminates choice A.

Examples

√18 ≠ 9, because 9² = 81 ≠ 18 . . . . eliminates choice C.

√49 = 7 because 7² = 7(7) = 49, choice D.

√25 = 5 because 5² = 25, choice E.

The true statements are statements B, D, E.

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