Question

Estimate the square root to the nearest (a) whole number and (b) tenth. Make sure you list 2 answers for these problems.

square root of -220

Answer 1

• -15i
• -14.8i

Explanation:

(a)

The nearest squares to 220 are 14² = 196 and 15² = 225. Since 220 is closer to 225 than to 196, the nearest whole number to the square root of 220 is 15.

The square root of -220 is imaginary, so the nearest whole number value will be 15i.

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(b)

The decimal fraction part of the root can be estimated from the nearest squares to be ...

(220 -196)/(225 -196) ≈ 0.828

Then the root of 220 to the nearest tenth is 14.8. The root of -220 to the nearest tenth will be the imaginary number 14.8i.