Question

) 2√72×5√32×3√50 ம‌தி‌ப்பை‌க் கண‌க்‌கி‌ட்டு எ‌ளிய வடி‌வி‌ல் கா‌ண்க

Answer 1

7200$\sqrt{2}$

விளக்கம்:

i)2√72×5√32×3√50

$2 \sqrt{72} \times 5 \sqrt{32} \times 3 \sqrt{50}=$$(2 \times 6 \sqrt{2}) \times(5 \times 4 \sqrt{2}) \times(3 \times 5 \sqrt{2})$

                                  $=2 \times 5 \times 3 \times 6 \times 4 \times 5 \times \sqrt{2} \times$$\sqrt{2} \times \sqrt{2}$

                                 = 10 × 18 × 20 × $2 \sqrt{2}$

                                 = 3600 × $2 \sqrt{2}$

                                = 7200 $\sqrt{2}$

மதிப்பு = 7200 $\sqrt{2}$

Answer 2

$\huge{\underline{\underline{\bf{Solution}}}}$

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{To \: Find :}}}}$

We have to find the value of : $\sf{2\sqrt{72} \times 5\sqrt{32} \times 3\sqrt{50}}$

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{Explanation :}}}}$

Firstly, we will make prime factors of 72, 32 and 50.

$\sf{\sqrt{72} = \sqrt{2 \times 2 \times 2 \times 3 \times 3} = 6\sqrt{2}} \\ \\ \sf{\sqrt{32} = \sqrt{2 \times 2 \times 2 \times 2 \times 2} = 4\sqrt{2}} \\ \\ \sf{\sqrt{50} = \sqrt{2 \times 5 \times 5} = 2\sqrt{2}}$

$\rule{150}{2}$

Now, Putting Values

$\sf{\dashrightarrow 2 \times 6\sqrt{2} \times 5 \times 4\sqrt{2} \times 3 \times 5\sqrt{2}} \\ \\ \sf{\dashrightarrow 12 \sqrt{2} \times 20\sqrt{2} \times 15\sqrt{2}} \\ \\ \sf{\dashrightarrow 240 \times 2 \times 15\sqrt{2}} \\ \\ \sf{\dashrightarrow480 \times 15\sqrt{2}} \\ \\ \sf{\dashrightarrow 7200\sqrt{2}}$

$\Large{\star{\boxed{\sf{7200 \sqrt{2}}}}}$

$\rule{400}{4}$

Prime factorisation of 72

$\begin{array}{r | l} 2 & 72 \\ \cline{1-2} 2 & 36 \\ \cline{1-2} 2 & 18 \\ \cline{1-2} 3& 9 \\ \cline{1-2} 3 & 3 \\ \cline{1-2} & 1 \end{array}$

$\rule{200}{2}$

Prime factorisation of 50

$\begin{array}{r | l} 2 & 432 \\ \cline{1-2} 2 & 50 \\ \cline{1-2} 5 & 25 </p><p> \\ \cline{1-2} 5 & 5 \\ \cline{1-2} & 1 \end{array}$

$\rule{200}{2}$

Prime factorisation of 32

$\begin{array}{r | l} 2 & 32 \\ \cline{1-2} 2 & 16 \\ \cline{1-2} 2 & 8 \\ \cline{1-2} 2 & 4 \\ \cline{1-2} 2 & 2 \\ \cline{1-2} & 1 \end{array}$