Question

between what 2 integers the square root of the numbers can be found
1. 23
2. 113
3. 339
4. 640
5. 75

Answer 1

Answer:

1.4-5

2.10-11

3.18-19

4.25-26

5.8-9

Answer 2

Answer:

1. 4 and 5

2. 10 and 11

3.18 and 19

4.25 and26

5.8 and 9

Step-by-step explanation:

Step 1:

The square root of the given number is lies between two integer

let a and b be the integer.

c is the given number.

Step 2:

To find $a^{2}\leq \sqrt[]{c} \leq b^{2}$

1. 23

c=23

$16\leq 23\leq 25$

$4^{2}\leq \sqrt[]{c} \leq 5^{2}$

Therefore, 23 lies between the integer 4 and 5.

2. 113

c=133

$100\leq 113\leq 121$

$10^{2}\leq \sqrt[]{113} \leq 11^{2}$

Therefore, the square root of 113 lies between the integer 10 and 11.

3. 339

c=339

$324\leq 339\leq 361$

$18^{2}\leq \sqrt[]{339} \leq 19^{2}$

Therefore, the square root 339 lies between the integers 18 and 19.

4. 640

c=640

$625\leq 640\leq 676$

$25^{2}\leq \sqrt[]{640} \leq 26^{2}$

Therefore, the square root 640 lies between the integers 25 and 26.

5.75

c=75

$64\leq 75\leq 91$

$25^{2}\leq \sqrt[]{640} \leq 26^{2}$

Therefore, the square root 75 lies between the integers 8 and 9.