Question

Estimate the square root of 14 to two decimal places

Answer 1

Answer:

3.74

Step-by-step explanation:

First, we can place the square root of fourteen between it's two closest square roots:

√9 < √14 < 16

3 < √14 < 4

Now since 14 is closer to 16 than 9, we can do this:

3.9^2 = 15.21

3.8^2 = 14.44

3.7^2 = 13.69

We can see that √14 must be between 13.69, and 14.44, which are 3.7^2 and 3.8^2, so we know that √14 must be between those numbers. If we go even further, then:

3.72^2 = 13.83

3.73^2 = 13.91

3.74^2 = 13.98

3.75^2 = 14.06

We can see that 3.74^2 is the closest to 14, only .02 away from the actual number, so 3.74 is our estimate for the square root of fourteen.

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