Estimating √30 Between Two Perfect Squares

0:00What is the square root of 30? Let us estimate it without a calculator.

0:05The square root of 30 is the number that makes 30 when it is multiplied by itself.

0:13A perfect square is a whole number times itself, like 5 times 5 is 25, and 6 times 6 is 36.

0:22On a number line, 30 lies between the perfect squares 25 and 36.

0:29The square roots of 25 and 36 are 5 and 6, so the square root of 30 lies between 5 and 6.

0:3830 is 5 past 25 but 6 short of 36, so its square root should be a little closer to 5.

0:47A common mistake is to guess exactly halfway, 5.5, without checking.

0:53Check it by squaring, which means multiplying it by itself. 5.5 times 5.5 is 30.25.

1:0330.25 is just over 30, so 5.5 is a little too big. The square root of 30 is just under 5.5.

1:14Now zoom in between 5.4 and 5.5. Each small step is one hundredth.

1:21Try a little less. 5.48 times 5.48 is 30.0304, still just over 30.

1:31Now try 5.47. 5.47 times 5.47 is 29.9209, just under 30.

1:42So the square root of 30 lies between 5.47 and 5.48.

1:48A calculator gives 5.4772 for the square root of 30, and the digits keep going.

1:56Rounded to two decimal places, the square root of 30 is about 5.48.

2:02To estimate a square root, find the perfect squares on either side, then square your guess to check it.