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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