What is the approximate value of the square root of 13?

To determine the square root of 13, let's first recognize that it lies between the square roots of perfect squares that are closest to 13. The perfect squares directly around 13 are 9 (which has a square root of 3) and 16 (with a square root of 4). Therefore, the square root of 13 is approximately between 3 and 4.

A more precise way to estimate the square root is to consider the values of 3.5 and 3.6. Squaring these values gives:

• ( 3.5^2 = 12.25 ) (which is less than 13)

• ( 3.6^2 = 12.96 ) (which is still less than 13)

• ( 3.7^2 = 13.69 ) (which exceeds 13)

From this analysis, we can infer that the square root of 13 must fall between 3.6 and 3.7. Since ( 3.6^2 ) is closer to 13 than ( 3.5^2 ), we can say that the square root of 13 is a bit more than 3.6.

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