Question

Between which two consecutive integers does square root of 150 lie

Answer 1

Step-by-step explanation:

144< 150 < 169

12² < 150 < 13²

Therefore, Square root of 150 lies between 12 and 13

Answer 2

The square root of 150 lies between the consecutive integers 12 and 13.

Square Root :

• The square root of a number "X" is a number "Y" that satisfies some condition
• The product of Y to itself twice results in X
• The square root is denoted as :

                    $\sqrt{X} = Y$

                       $X = Y^{2}$

                       $X = Y * Y$

Finding Square Root of 150 :

Firstly, we do the Prime Factorization of 150 :

          $150 = 2 * 3 * 5 * 5$

Grouping common terms leads to finding factors of the square root of the number.

           $150 = 2 * 3 * 5 * 5\\\sqrt{150} = \sqrt{2*3*5*5} \\\sqrt{150} = \sqrt{2*3*5^{2} }\\ \sqrt{150} = \sqrt{2*3} * \sqrt{ 5^{2} } \\ \sqrt{150} = \sqrt{6} * 5\\\sqrt{150}= 2.45 * 5\\\sqrt{150}= 12.25$

Thus, the decimal value 12.25 lies between the two integers 12 and 13.

Also, the square of 12 $= 12 * 12 =144$

The square of 13 $= 13 * 13 = 169$

                  $144 < 150 < 169\\\sqrt{144} < \sqrt{150} < \sqrt{169}\\ 12 < \sqrt{150} < 13$

Hence, the square root of 150 lies between the integers 12 and 13.

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