Question

State if true or false
Ten times the square root of 42.25 is 65.

Answer 1

Hint: Here we will use the long division method to find the square root and then multiply it by ten to get the value and then check whether it matches the given value.
If it matches then the given statement would be true otherwise it would be false.
Long division method is used to divide a large number (usually three digits or more) by a number having two or more digits.

Complete step-by-step answer:
Here first we have to find the square root of 42.25
Hence we will apply the long division method to get the square root.
Applying long division method we get:-
First we will place a bar over the pair of numbers starting from the unit place and also the decimals.
\[ = \sqrt {\overline {42} .\overline {25} } \]
Now we will take the largest number as the divisor whose square is less than or equal to 42 then divide and write the quotient.
\[
  6\mathop{\left){\vphantom{1{\overline {42} .\overline {25} }}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{{\overline {42} .\overline {25} }}}}
\limits^{\displaystyle \,\,\, 6} \\
   - 36 \\
   \cdots \cdots \cdots \cdots \\
  6 \\
   \cdots \cdots \cdots \cdots \\
 \]
Now we will bring down 0.25, which is under the bar, to the right side of the remainder and double the value of the quotient and enter it with blank space on the right side. Next, we have to select the largest digit for the unit place of the divisor such that the new number, when multiplied by the new digit at unit’s place, is equal to or less than 6.25.
\[
  12.5\mathop{\left){\vphantom{1{6.25}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{{6.25}}}}
\limits^{\displaystyle \,\,\, {0.5}} \\
  {\text{ }} - 6.25 \\
   \cdots \cdots \cdots \cdots \cdots \\
  {\text{ 0}} \\
 \]
Now since we got zero as remainder therefore we can now write the quotient.
Since our first quotient was 6 and another quotient was 0.5
Hence the final quotient is 6.5.
Therefore the square root of 42.25 is 6.5
Now we will multiply the root so obtained by ten to check whether the given statement is true or false.
Hence multiplying 6.5 by 10 we get:-
\[ = 6.5 \times 10\]
Shifting the decimal place to right as the number is multiplied by 10 we get:-
\[ = 65\]
Hence the statement, ten times square root of 42.25 is 65 is true.

Note: The student may make mistakes while selecting the right quotient, so one should follow the steps of the long division method carefully and should continue the process until the remainder comes out to be zero.