Tag: approximation of square roots

Questions Related to approximation of square roots

Find the least number which must be subtracted from each of the following numbers so as to get a perfect square Also find the square root of the perfect square so obtained 
$(i) 402, (ii) 1989, (iii) 3250, (iv) 825, (v) 4000$

maths squares and square roots approximation of square roots estimating square roots square root of non perfect squares

  1. Least number which must be subtracted:$(i) 2, (ii) 22, (iii) 1, (iv) 21, (v) 52$

    Square root of the perfect square:
    $(i) 20, (ii) 34 ,(iii) 55, (iv) 26, (v) 67$

  2. Least number which must be subtracted:$(i) 2, (ii) 53, (iii) 1, (iv) 41, (v) 31$

    Square root of the perfect square:
    $(i) 20, (ii) 44, (iii) 57, (iv) 28, (v) 63$

  3. Least number which must be subtracted:$(i) 6, (ii) 22, (iii) 50, (iv) 31, (v) 40$

    Square root of the perfect square:
    $(i) 19, (ii) 41, (iii) 49 ,(iv) 27 ,(v) 65$

  4. Least number which must be subtracted:$(i) 8, (ii) 41, (iii) 12, (iv) 56, (v) 4$

    Square root of the perfect square:
    $(i) 19 ,(ii) 22, (iii) 37, (iv) 26, (v) 61$

Show answer
Correct Option: B
Explanation:

For $402$

Nearest perfect square is $400$
$\sqrt{400}$ $=$ $20$
$402$ $-$ $400$ $=$ $2$
For $1989$
Nearest perfect square is $1936$

$\sqrt{1936}$ $=$ $44$
$1936$ $-$ $1989$ $=$ $53$

For $3250$
Nearest perfect square is $3249$

$\sqrt{3249}$ $=$ $57$
$3250$ $-$ $3249$ $=$ $1$
For $825$
Nearest perfect square is $784$
$\sqrt{784}$ $=$ $28$
$825$ $-$ $784$ $=$ $41$
For $4000$
Nearest perfect square is $3969$
$\sqrt{3969}$ $=$ $63$
$4000$ $-$ $3969$ $=$ $31$
From this, Option B is correct answer.

Mr. Hansraj wants to find the least number of boxes to be added to get a perfect square. He already has $7924$ boxes with him. How many more boxes are required?

maths squares and square roots approximation of square roots estimating square roots square root of non perfect squares

  1. $819$

  2. $412$

  3. $419$

  4. $176$

Show answer
Correct Option: D
Explanation:

Find square root by long division method.

$\therefore \sqrt {7924}$ = $89.01$

Hence, the perfect square number smaller than $7924$ is
$89^2 = 7921$
The next perfect square no. is $90^2 = 8100$

So, $8100 - 7924 = 176$
Therefore, the man needs $176$ more boxes in order to get a perfect square number.
So, option D is correct.

$\displaystyle \sqrt { 4.8\times { 10 }^{ 9 } } $ is closest in value to

maths squares and square roots approximation of square roots estimating square roots square root of non perfect squares

  1. $2200$

  2. $70000$

  3. $220000$

  4. $7000000$

  5. $22000000$

Show answer
Correct Option: B
Explanation:

$\displaystyle \sqrt { 4.8\times { 10 }^{ 9 } } $

$=\sqrt{48\times10^{8}}$$\simeq$$7\times10^{4}=70000$
$7^{2}$$=$$49$
Hence Option B is correct.

What is an approximate value of $\sqrt{9805}$?

maths squares and square roots approximation of square roots estimating square roots square root of non perfect squares

  1. 98.56

  2. 97.23

  3. 99.05

  4. 100.34

Show answer
Correct Option: C
Explanation:

$99^2$ = 9801
$100^2$ = 10000
In between this two squares, 9805 is placed.
So the average of $\frac{99 + 100}{2}= 99.5$
Then, $99.5^2 = 9900.25$
So, $\sqrt{9805} \approx 99.05$

Estimate the square root of 500.

maths squares and square roots approximation of square roots estimating square roots square root of non perfect squares

  1. 22.5

  2. 20.3

  3. 21.4

  4. 23.6

Show answer
Correct Option: A
Explanation:

$22^2$ = 484
$23^2$ = 576
In between this two square numbers, 500 is placed.
So average of $\frac{22 + 23}{2}= 22.5$
Then, $22.5^2 = 506.25$
So, $\sqrt{500} \approx 22.5$

Find the approximate value of $\sqrt{5245}$.

maths squares and square roots approximation of square roots estimating square roots square root of non perfect squares

  1. 70.5

  2. 72.3

  3. 71.8

  4. 79.2

Show answer
Correct Option: B
Explanation:

$72^2$ = 5184
$73^2$ = 5329
In between this two squares, 5245 is placed.
So average of $\frac{72 + 73}{2}= 72.5$
Then, $72.5^2 = 5256.25$
So, $\sqrt{5245} \approx 72.3$

Find the approximate value of $\sqrt{1235}$.

maths squares and square roots approximation of square roots estimating square roots square root of non perfect squares

  1. $35.15$

  2. $32.19$

  3. $30.25$

  4. $29.13$

Show answer
Correct Option: A
Explanation:

$35^2$ = 1225
$36^2$ = 1296
In between this two squares, 1235 is placed.
So the average of $\dfrac{35 + 36}{2}= 35.5$
Then, $35.5^2 = 1260.25$

So $\sqrt{1235}\approx35.15$

Estimate the value of $\sqrt{750}$.

maths squares and square roots approximation of square roots estimating square roots square root of non perfect squares

  1. 24.3

  2. 25.1

  3. 23.2

  4. 27.3

Show answer
Correct Option: D
Explanation:

$27^2$ = 729
$28^2$ = 784
In between this two squares, 750 is placed.
So average of $\frac{27 + 28}{2}= 27.5$
Then, $27.5^2 = 756.25$
So, $\sqrt{750} \approx 27.3$

Estimate the square root of $300$

maths squares and square roots approximation of square roots estimating square roots square root of non perfect squares

  1. $12.44$

  2. $16.66$

  3. $17.32$

  4. $18.54$

Show answer
Correct Option: C
Explanation:

The square root of $300$ is $10\sqrt 3$

We know that $\sqrt 3=1.732$
Thus $\sqrt{300}=10\times 1.732=17.32$

Estiamate the square root of $850$ 

maths squares and square roots approximation of square roots estimating square roots square root of non perfect squares

  1. $29.15$

  2. $30.21$

  3. $98.23$

  4. $23.11$

Show answer
Correct Option: A
Explanation:

The square root of $850$ is $\sqrt {850}=\sqrt {25 \times 34}=5\sqrt {34}$

Square root of $34$ lie between $5$ and $6$.
 square of $5.5$ is $30.25$ 
Now, we can say that square root of $34$ lie between $5.5$ and $6$.
Now, square of $5.75$ is $33.06$
So, square root of $34$ lie between $5.75$ and $6$.
Now, we have to choose the number $5.85$
$(5.85)^2=34.225$ which is greater than $34$ and close to $34$
So, assume a number $5.84$.
$(5.84)^2=34.1056$
$(5.83)^2=33.9889$
Hence, we can say that square root of 34 lie between $5.83$ and $5.84$.
So, $5\times 5.83=29.15$.