Questions & Answers

Question

Answers

(a)2.64

(b)2.55

(c)2.67

(d)2.72

Answer
Verified

Hint: Use the steps of the square root by long division method to find the square root of a given problem.

__Complete step-by-step answer:__

We have to find the square root of 7 correct to 2 decimal places.

First we write the steps of doing long division method for finding square roots:

Step 1: First group the digits in pairs, starting with the digit in units place. Each pair and the remaining digit (if any) is called a period.

Step 2: Think of the largest number whose square is equal to or just less than the first period. Taking this number as a divisor and also the quotient.

Step 3: Subtract the product of the divisor and the quotient from the first period and bring down the next period to the right of the remainder. This makes a new dividend.

Step 4: Now, the divisor is obtained by taking two times the quotient and annexing the suitable digit which is also t when as the next digit of quotient, chosen in such a way that the product of new divisor and the digits are equal or just less than the new dividend.

Step 5: Repeat steps (2), (3), (4) till all the periods have been taken up. Now the quotient so obtained is the required square root of the given number.

Let us take an example of finding square root of 784,

Here, the square root is 28.

Step 6 (additional): This is only if we have to find the square root after decimal. So, after every period is exhausted we will put a decimal as quotient and bring down 2 zeroes and if the divisor is big then we will bring two more.

Now let’s take number 7.

In the question we have been asked for two decimal places so we get square root equals to 2.64.

So, the correct option is (a).

Note: Students generally don’t know clearly how to do square root by division method, hence they should follow the steps in the solution so that the concept becomes clear. They should also do calculations clearly to avoid any errors.

We have to find the square root of 7 correct to 2 decimal places.

First we write the steps of doing long division method for finding square roots:

Step 1: First group the digits in pairs, starting with the digit in units place. Each pair and the remaining digit (if any) is called a period.

Step 2: Think of the largest number whose square is equal to or just less than the first period. Taking this number as a divisor and also the quotient.

Step 3: Subtract the product of the divisor and the quotient from the first period and bring down the next period to the right of the remainder. This makes a new dividend.

Step 4: Now, the divisor is obtained by taking two times the quotient and annexing the suitable digit which is also t when as the next digit of quotient, chosen in such a way that the product of new divisor and the digits are equal or just less than the new dividend.

Step 5: Repeat steps (2), (3), (4) till all the periods have been taken up. Now the quotient so obtained is the required square root of the given number.

Let us take an example of finding square root of 784,

Here, the square root is 28.

Step 6 (additional): This is only if we have to find the square root after decimal. So, after every period is exhausted we will put a decimal as quotient and bring down 2 zeroes and if the divisor is big then we will bring two more.

Now let’s take number 7.

In the question we have been asked for two decimal places so we get square root equals to 2.64.

So, the correct option is (a).

Note: Students generally don’t know clearly how to do square root by division method, hence they should follow the steps in the solution so that the concept becomes clear. They should also do calculations clearly to avoid any errors.

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