Question

By which least number should 6534 should be divided to get a perfect square? Also find the square root of the resulting number.



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Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The Least number by which 6534 should be divided is 6. The resulted Number is 1089 and its Square root is 33.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

The Number = 6,534

To Find :

• Least number by which 6534 should be divided to get a perfect square
• Square root of the resulting number.

Solution :

★ $\textbf{Prime Factorize 6534}$

$\begin{array}{r|l} 2 & 6534 \\\cline{1-2} 3 & 3267 \\\cline{1-2} 3 & 1089 \\ \cline{1-2} 3 & 363 \\\cline{1-2} 11 & 121 \\\cline{1-2} 11 & 11 \\\cline{1-2} & 1 \end{array}$

6534 = 2 × 3 × 3 × 3 × 11 × 11

The Numbers 2 and 3 are not in pair. The product of the unpaired numbers should be divided by 6534 to get a Perfect Square.

$\longrightarrow$ 2 × 3

$\longrightarrow$ 6

$\rule{300}{1.5}$

Divide 6534 by 6 to get the Perfect Square.

$\longrightarrow$ 6534 ÷ 6

$\longrightarrow$ 1089

The Number resulted is 1089.

$\rule{300}{1.5}$

★ $\textbf{Square root of 1089 :-}$

Prime Factorize 1089

$\begin{array}{r|l} 3 & 1089 \\ \cline{1-2} 3 & 363 \\\cline{1-2} 11 & 121 \\\cline{1-2} 11 & 11 \\\cline{1-2} & 1 \end{array}$

$\longrightarrow$ 1089 = 3 × 3 × 11 × 11

$\longrightarrow$ $\sf{\sqrt{1089}}$ = 3 × 11

$\longrightarrow$ $\sf{\sqrt{1089}}$ = 33

$\therefore$ The Least number by which 6534 should be divided is 6. The resulted Number is 1089 and its Square root is 33.

Answer 2

Answer —

prime Factorize 6534

2 | 6534

3 | 3267

3 | 1089

3 | 363

11 | 121

11 | 11

| 1

6534 = 2 × 3 × 3 × 3 × 11 × 11

==> 3 × 2

==> 6

6534 ÷ 6

==> 1089

The number is 1089

Square root of 1089

3 | 1089

3 | 363

11 | 121

11 | 11

| 1

==> 3 × 3 × 11 × 11

==> 3 × 11

==> 33

The number should be divided by 6. √1089 = 33