Question

Estimate the following square roots.
A) 13
B) 90
c) 70
d) 50

Answer 1

To estimate the square roots of 13, 90, 70, and 50, one must find the nearest perfect squares to these numbers and determine the range within which the square root lies, approximating to the more immediate perfect square based on proximity.

Step-by-step explanation:

The student has asked to estimate the following square roots: 13, 90, 70, and 50. We need to find the nearest perfect squares to each number to make an estimate.

• The square root of 13 is between the square roots of 9 (32=9) and 16 (42=16). So, √13 is approximately between 3 and 4.
• The square root of 90 is between the square roots of 81 (92=81) and 100 (102=100). So, √90 is close to 9 but slightly more because 90 is closer to 100 than to 81.
• The square root of 70 is between the square roots of 64 (82=64) and 81 (92=81). Therefore, √70 is about between 8 and 9, leaning towards 8 since 70 is closer to 64.
• Last, The square root of 50 is between the square roots of 49 (72=49) and 64 (82=64). So, √50 is approximately between 7 and 8, but closer to 7 since 50 is just one unit above 49.