Question

How do you find the square root of \[14,400?\]

Answer 1

Hint:The given question involves the operation of addition/ subtraction/ multiplication/ division. To solve these types of problems we need to know the square values of basic terms. It doesn’t involve any arithmetic formulae, it is completely involved in arithmetic operations. We need to know the process of finding the square root of the given term without using a scientific calculator.

Complete step by step solution:
In this question, we would find the square root value \[14,400\] without using a calculator. The following steps show the operations of finding the square root of \[14,400\].
\[divisor\mathop{\left){\vphantom{1{dividend}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{{dividend}}}}
\limits^{\displaystyle \,\,\, {quotient}}\]
\[1\mathop{\left){\vphantom{1
14400 \\
1 \\
22\left){\vphantom{1
044 \\
44 \\
440\left){\vphantom{1
000 \\
00 \\
\Rightarrow 0 \\
}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{
000 \\
00 \\
\Rightarrow 0 \\
}} \\
}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{
044 \\
44 \\
440\left){\vphantom{1
000 \\
00 \\
\Rightarrow 0 \\
}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{
000 \\
00 \\
\Rightarrow 0 \\
}} \\
}} \\
}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{
14400 \\
1 \\
22\left){\vphantom{1
044 \\
44 \\
440\left){\vphantom{1
000 \\
00 \\
\Rightarrow 0 \\
}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{
000 \\
00 \\
\Rightarrow 0 \\
}} \\
}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{
044 \\
44 \\
440\left){\vphantom{1
000 \\
00 \\
\Rightarrow 0 \\
}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{
000 \\
00 \\
\Rightarrow 0 \\
}} \\
}} \\
}}}
\limits^{\displaystyle \,\,\, {120}}\]
First, we have to solve the first number \[1\] \[14400\]. As a next step, we have to find the square root \[1\]. So, we know that the square root of \[1\] is \[1\]. So, let’s write \[1\] as a divisor and quotient.
\[1\mathop{\left){\vphantom{1
14400 \\
1 \\
}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{
14400 \\
1 \\
}}}
\limits^{\displaystyle \,\,\, 1}\]
When we subtract\[1\]and\[1\], we get zero. Next, we drop the next two numbers.
\[1\mathop{\left){\vphantom{1
14400 \\
1 \\
22\left){\vphantom{1
044 \\
44 \\
}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{
044 \\
44 \\
}} \\
}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{
14400 \\
1 \\
22\left){\vphantom{1
044 \\
44 \\
}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{
044 \\
44 \\
}} \\
}}}
\limits^{\displaystyle \,\,\, {12}}\]
The first divisor is multiplied with\[2\]and take as the first digit of the second divisor. So, we
put\[2\]as a divisor and quotient. So, we get\[22\]as a nest divisor. After
subtracting\[44\]and\[44\]we get\[0\].
\[1\mathop{\left){\vphantom{1
14400 \\
1 \\
22\left){\vphantom{1
044 \\
44 \\
440\left){\vphantom{1
000 \\
00 \\
\Rightarrow 0 \\
}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{
000 \\
00 \\
\Rightarrow 0 \\
}} \\
}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{
044 \\
44 \\
440\left){\vphantom{1
000 \\
00 \\
\Rightarrow 0 \\
}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{
000 \\
00 \\
\Rightarrow 0 \\
}} \\
}} \\
}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{
14400 \\
1 \\
22\left){\vphantom{1
044 \\
44 \\
440\left){\vphantom{1
000 \\
00 \\
\Rightarrow 0 \\
}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{
000 \\
00 \\
\Rightarrow 0 \\
}} \\
}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{
044 \\
44 \\
440\left){\vphantom{1
000 \\
00 \\
\Rightarrow 0 \\
}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{
000 \\
00 \\
\Rightarrow 0 \\
}} \\
}} \\
}}}
\limits^{\displaystyle \,\,\, {120}}\]
The last digit of the second divisor is multiplied by two and taken as the first two digits of the third divisor. Next, we drop two zero from the dividend. So, we know that \[0 \times 0\] is \[0\]. So, let’s take \[0\] a quotient as a part of the divisor.
So, the final answer is,
The square root \[14400\] is equal to \[120\].

Note: For finding the square root of a given value we use the operation of addition/ subtraction/ multiplication/ division. If the negative sign is involved inside the square root consider it as a positive number and follow the above-mentioned operation by adding \[i\]with a final answer for a negative sign of square root term. For each next step, we would multiply the last digit of the divisor by\[2\].