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Step-by-step explanation

There are two ways to evaluate this. The two methods are related too.

First method is just to use a calculator. This is the easier method.

√37 = 6.083, hence, √37 is between 6 and 7.

√2 = 1.414, hence, √2 is between 1 and 2.

√350 = 18.708, hence, √350 is between 18 and 19.

√500 = 22.361, hence, √500 is between 22 and 23.

√60 = 7.746, hence, √60 is between 7 and 8.

The second method is to note the closest perfect squares to these numbers. One wouldn't need a calculator for this.

Note that a perfect square is a number that has a whole number square root, that is, a number, whose square root is whole number.

√230

230 is bounded on both sides by the perfect squares 225 and 256.

225 = 15²

256 = 16²

So, √230 is between 15 and 16.

√190

190 is bounded on both sides by the perfect squares 169 and 196.

169 = 13²

196 = 14²

So, √190 is between 13 and 14.

√5

5 is bounded on both sides by the perfect squares 4 and 9.

4 = 2²

9 = 3²

So, √5 is between 2 and 3.

√115

115 is bounded on both sides by the perfect squares 100 and 121.

100 = 10²

121 = 11²

So, √115 is between 10 and 11.

√90

90 is bounded on both sides by the perfect square 81 and 100.

81 = 9²

100 = 10²

So, √90 is between 9 and 10.

Hope this Helps!!!

User John Bowyer
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