Question

find the square root of the following decimal numbers (1)1056.25 (2)10020.01 explain step by step ​

Answer 1

ANSWER:

• √(1056.25) = 32.5

• √(10020.01) = 100.1

GIVEN:

The numbers are:

• 1056.25

• 10020.01

TO FIND:

• The square root of the numbers.

EXPLANATION:

$\begin{array} {c|c} \sf\underline{ \ \ 5 \ \ }&\sf\underline{ \ \ \ 1056.25\ \ \ } \\\sf \underline{ \ \ 5 \ \ }&\sf\underline{ \ \ \ 211.25\ \ \ } \\ \sf\underline{ \ \ 5 \ \ }&\sf\underline{ \ \ \ 42.25\ \ \ } \\\sf \underline{ \ \ 5 \ \ }&\sf\underline{ \ \ \ 8.45\ \ \ } \\\sf\underline{ \ \ 1.3\ \ }&\sf\underline{ \ \ \ 1.69\ \ \ } \\\sf \underline{ \ \ 1.3 \ \ }&\sf\underline{ \ \ \ 1.3\ \ \ } \\ &\sf\underline{ \ \ \ 1\ \ \ } \end{array} \\ \\ \\ \sf \leadsto 1056.25 = 5 \times 5 \times 5 \times 5 \times 1.3 \times 1.3 \\ \\ \\ \textbf{ \underline{Take square root on both sides}} \\ \\ \\ \sf \leadsto \sqrt{1056.25} = \sqrt{5 \times 5 \times 5 \times 5 \times 1.3 \times 1.3} \\ \\ \\ \sf \leadsto\sqrt{1056.25} = 5 \times 5 \times 1.3 \\ \\ \\ \sf \leadsto \sqrt{1056.25} = 32.5$

$\over{\qquad \qquad\qquad\qquad\qquad \qquad\qquad\qquad\qquad}$

$\begin{array} {c|c}\sf \underline{ \ \ 13 \ \ }&\sf\underline{ \ \ \ 10020.01\ \ \ } \\\sf \underline{ \ \ 13 \ \ }&\sf\underline{ \ \ \ 770.77\ \ \ } \\ \sf\underline{ \ \ 7 \ \ }&\sf\underline{ \ \ \ 59.29\ \ \ } \\ \sf\underline{ \ \ 7\ \ }&\sf\underline{ \ \ \ 8.47\ \ \ } \\\sf\underline{ \ \ 1.1\ \ }&\sf\underline{ \ \ \ 1.21\ \ \ } \\ \sf\underline{ \ \ 1.1 \ \ }&\sf\underline{ \ \ \ 1.1\ \ \ } \\&\sf\underline{ \ \ \ 1\ \ \ } \end{array} \\ \\ \\ \sf \leadsto 10020.01= 13 \times 13 \times 7 \times 7 \times 1.1 \times 1.1 \\ \\ \\ \textbf{ \underline{Take square root on both sides}} \\ \\ \\ \sf \leadsto \sqrt{10020.01} = \sqrt{13 \times 13 \times 7 \times 7 \times 1.1 \times 1.1} \\ \\ \\ \sf \leadsto\sqrt{10020.01} = 13 \times 7 \times 1.1 \\ \\ \\ \sf \leadsto\sqrt{10020.01} = 100.1$

$\bigstar\ \boxed{\begin{minipage}{3 cm} \mathsf{\sqrt{1056.25} = 32.5}\\ \\ \mathsf{\sqrt{10020.01} = 100.1} \end{minipage}}$

Answer 2

Given :   (1)1056.25 (2)10020.01

To Find : Square root

Solution:

               32.5

  3         1056.25

              9

           ____

             156

 62        124

              ____

                3225

645          3225

               ______

                       0

√ 1056.25  = 32.5

Other method :

1056.25 = 105625 / 100

105625  = 5 * 5 * 5 * 5 * 13 * 13  = 5² * 5²  * 13²

100 = 10²

√1056.25   = 5 * 5 * 13 /10

= 65/2

= 32.5

Similarly  √10020.01  =  100.1

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