QuestionWhat is the closest approximation of $\sqrt{53}$ from the options: 8.1, 7.3, 7.1, 7.7?

Studdy Solution

STEP 1

Assumptions1. We are asked to approximate the square root of53. We have four options8.1,7.3,7.1,7.7

STEP 2

To find the best approximation, we can square each of the options and see which one is closest to53.
$Square\, of\, each\, option = Option^2$

STEP 3

Calculate the square of each option.
$Square\, of\,8.1 =8.1^2$ $Square\, of\,7.3 =7.3^2$ $Square\, of\,7.1 =7.1^2$ $Square\, of\,7.7 =7.7^2$

STEP 4

Calculate the square of8.1.
$Square\, of\,8.1 =8.1^2 =65.61$

STEP 5

Calculate the square of7.3.
$Square\, of\,7.3 =7.3^2 =53.29$

STEP 6

Calculate the square of.1.
$Square\, of\,.1 =.1^2 =50.41$

STEP 7

Calculate the square of7.7.
$Square\, of\,7.7 =7.7^2 =59.29$

STEP 8

Now that we have the square of each option, we can compare these values to53 to see which one is closest.

STEP 9

The square of7.3 is closest to53.
So, the best approximation of $\sqrt{53}$ is7.3.

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