Module 5 Real Numbers Test

• 2; positive and negative

• 1; positive

• none; no solution

Answer explanation

The square root of a number, like √100, has two solutions: +10 and -10. Therefore, the correct answer is 2; positive and negative.

• 2; negative and positive

• 1; negative

• None; no soultion

Answer explanation

The expression -√49 equals -7. A negative square root has only one solution, which is negative. Therefore, the correct answer is 1; negative.

• 2; positive and negative

• 1; only negative

• None; no soultion

Answer explanation

A square root with a negative number inside the radical, like \sqrt[]{-36}, has no real solutions. Therefore, the correct answer is 'None; no solution'.

Why does a negative underneath a radical create a "no solution" answer in math?

• Negative numbers can be simplified to positive under a radical.

• Radicals with negatives are always solvable in the real number system.

• Because you cannot multiply the same number to get a negative answer, you will end up with positive every time.

Answer explanation

A negative under a radical leads to no solution in the real number system because no real number squared gives a negative result. Thus, the only outcomes from squaring are positive or zero.

• 11

• -11

• -10

• -12

Answer explanation

To solve -√121, we first find √121, which is 11. The negative sign in front indicates we take the negative value, resulting in -11. Therefore, the correct answer is -11.

Answer explanation

The square root of 144 is 12. Since square roots can be both positive and negative, the correct answer is \pm12.

• No solution

• 0

Answer explanation

The expression \( \sqrt[]{-169} \) involves the square root of a negative number, which is not defined in the set of real numbers. Therefore, the correct answer is 'No solution'.

Find the area of the square with the given dimensions of 1.6 feet.

Find the area of the square with the given dimensions of 4 ft.