Question

find the square root of the following numbers by the prime factorisation method .
a)=7744
b) =9604
c)= 5929
d)=9216
e)= 529
f)=8100
plz slove the following questions .​

Answer 1

Step-by-step explanation:

a)

2|7744

2|3872

2|1936

2|968

2|484

2|242

11|121

11

______________________________

$\sqrt{7744} = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2\times 11 \times 11} \\ \sqrt{7744} = 2 \times 2 \times 2 \times 11 \\ 88$

b)

2|9604

2|4802

7|2401

7|343

7|49

7

___________________________________

$\sqrt{9604 }$= 2×2×7×7×7×7

$\sqrt{9604}$ = 2×7×7

$\sqrt{9604}$= 98

c)

7|5929

7|847

11|121

11

_____________________________

$\sqrt{5929}$ = 7×7×11×11

$\sqrt{5929}$ = 7×11 = 77

Answer 2

a) 7744

Step 1: Do prime factorization to get the product of primes.

$\begin{array}{r | l} 2 & 7744\\ \cline{2-2} 2 & 3872\\ \cline{2-2} 2 & 1936 \\ \cline{2-2} 2 & 968 \\ \cline{2-2} 2 & 484 \\\cline{2-2} 2 & 242 \\ \cline{2-2} 11 & 121 \\ \cline{2-2} & 11 \\ \end{array}$

∴ 7744 ⇒ $\sf 2\times 2\times 2\times 2\times 2\times 2\times 11 \times 11$

Step 2: Pair the product of primes.

$\sf (2\times 2)\times (2\times 2)\times (2\times 2)\times (11 \times 11)$

Step 3: Take one number from each pair and multiply to obtain the square root.

$\sf \sqrt{7744}=2\times 2 \times 2 \times 11$

$\sf \bf \therefore \ \sqrt{7744}=88$

$\rule{300}{0.5}$

b) 9604

Step 1: Do prime factorization to get the product of primes.

$\begin{array}{r | l}2 & 9604 \\ \cline{2-2} 2 &4802 \\ \cline{2-2} 7 &2401 \\ \cline{2-2} 7 & 343 \\\cline{2-2} 7& 49 \\\cline{2-2} & 7 \\ \end{array}$

∴ 9604 ⇒ $\sf 2\times 2\times 7\times 7\times 7\times 7$

Step 2: Pair the product of primes.

$\sf (2\times 2)\times( 7\times 7)\times (7\times 7)$

Step 3: Take one number from each pair and multiply to obtain the square root.

$\sf \sqrt{9604} = 2\times 7\times 7$

$\sf \bf \therefore \sqrt{9604} = 98$

$\rule{300}{0.5}$

c) 5929

Step 1: Do prime factorization to get the product of primes.

$\begin{array}{r | l} 7 & 5929 \\ \cline{2-2} 7 & 847 \\ \cline{2-2} 11 & 121 \\ \cline{2-2} & 11\\ \end{array}$

∴ 5929 ⇒ $\sf 7\times 7\times 11\times 11$

Step 2: Pair the product of primes.

$\sf (7\times 7)\times (11\times 11)$

Step 3: Take one number from each pair and multiply to obtain the square root.

$\sf \sqrt{5929} = 7\times 11$

$\sf \bf \therefore \sqrt{5929}=77$

$\rule{300}{0.5}$

d) 9216

Step 1: Do prime factorization to get the product of primes.

$\begin{array}{r | l} 2 & 9216\\ \cline{2-2} 2 & 4608\\ \cline{2-2} 2 & 2304 \\ \cline{2-2} 2 & 1152 \\\cline{2-2} 2 & 576 \\ \cline{2-2} 2 & 288 \\\cline{2-2} 2 & 144\\\cline{2-2} 2 & 72\\ \cline{2-2} 2 & 36 \\ \cline{2-2} 2&18 \\\cline{2-2} 3 & 9 \\\cline{2-2} & 3 \\\end{array}$

∴ 9216 ⇒ $\sf 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2 \times 2\times 2 \times 3\times 3$

Step 2: Pair the product of primes.

$\sf (2\times 2)\times (2\times 2)\times( 2\times 2)\times (2\times 2) \times (2\times 2) \times (3\times 3)$

Step 3: Take one number from each pair and multiply to obtain the square root.

$\sf \sqrt{9216}=2\times 2\times 2\times 2\times 2 \times 3$

$\sf \bf \therefore \sqrt{9216}=96$

$\rule{300}{0.5}$

e) 529

Step 1: Do prime factorization to get the product of primes.

$\begin{array}{r | l} 23 & 529 \\ \cline{2-2} & 23 \\ \end{array}$

∴ 539 ⇒ $\sf 23\times 23$

Step 2: Pair the product of primes.

$\sf (23\times 23)$

Step 3: Take one number from each pair and multiply to obtain the square root.

$\sf \bf \therefore \sqrt{529} = 23$

$\rule{300}{0.5}$

f) 8100

Step 1: Do prime factorization to get the product of primes.

$\begin{array}{r | l} 2 & 8100\\ \cline{2-2} 2 & 4050 \\ \cline{2-2} 3 &2025 \\ \cline{2-2} 3 & 675\\\cline{2-2} 3 & 225 \\ \cline{2-2} 3 & 75 \\ \cline{2-2} 5 & 25 \\\cline{2-2} &5 \\ \end{array}$

∴ 8100 ⇒ $\sf 2\times 2\times 3\times 3\times 3\times 3\times 5\times 5$

Step 2: Pair the product of primes.

$\sf (2\times 2) \times (3\times 3) \times (3\times 3) \times (5\times 5)$

Step 3: Take one number from each pair and multiply to obtain the square root.

$\sf \sqrt{8100} = 2\times 3\times 3\times 5$

$\sf \bf \therefore \sqrt{8100} = 90$

$\rule{300}{0.5}$