Question

estimate the square root of the following numbers upto one decimal point:150 ? please give answer with solution the answer is 12.2​

Answer 1

SOLUTION

TO DETERMINE

Estimate the square root of the number : 150

EVALUATION

Here the given number is 150

We now prime factorise the given number

150 = 2 × 3 × 5 × 5 = 2 × 3 × 5²

Thus we get

$\sqrt{150}$

$= \sqrt{2 \times 3 \times {5}^{2} }$

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

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

$= 5 \times 1.414 \times 1.732$

$= 12.24$

$\approx \: 12.2$

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Answer 2

To Find :- Square root of 150 upto one decimal place .

Solution :-

Finding the square root of 150 by long divison method we get,

Step 1) :- In order to make two pairs use decimal and after decimal put two zero . so, number is 150.00 . Now, our pairs from right end are :-

• 1 - 50 - 00

Step 2) :- Extreme left pair is our first dividend . Taking largest number as divisor we get,

1 ) 1 ( 1

-1

0

we get,

• Quotient = 1
• Remainder = 0

Step 3) :- Taking next pair on right side as dividend now which is 50 . Also, double the value of the quotient from first pair which is 1 and enter one blank space .

2_ ) 50 (

taking largest number in blank and multiply it by like (2_) * (_) such that, number will be less than or equal to 50 .

• 21 * 1 = 21
• 22 * 2 = 44
• 23 * 3 = 69 > 50 .

so, taking 44 ,

22 ) 50 ( 2

-44

6

we get,

• Quotient = 2
• Remainder = 6

Step 4) :- Taking next pair on right side with remainder 6 as dividend now, which becomes (600) and again, divisor will be (22 + 2) = 24_ . { Double of quotient in step 3 .}

24_ ) 600 (

again, taking larget number such that number will be less than or equal to 600 .

• 241 * 1 = 241
• 242 * 2 = 484
• 243 * 3 = 729 > 600

so, taking 484 ,

242 ) 600 ( 2

-484

116

we get,

• Quotient = 2
• Remainder = 116

therefore, writing all quotients together now, we get,

→ √150 ≈ 12.2 (Ans.)

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