Tag: squares and square roots

Questions Related to squares and square roots

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, $5\times 5.83=29.15$.

The real number $(\sqrt [3]{\sqrt {75} - \sqrt {12}})^{-2}$ when expressed in the simplest form is equal to

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

  1. $\dfrac {1}{2}$

  2. $\dfrac {1}{3}$

  3. $\dfrac {1}{4}$

  4. $\dfrac {1}{5}$

Show answer
Correct Option: B
Explanation:

Real number $(\sqrt[3]{\sqrt{75}-\sqrt{12}})^{-2}$

$\sqrt{75}=5\sqrt{3}$ and $\sqrt{12}=2\sqrt{3}$
$=(\sqrt[3]{5\sqrt{3}-2\sqrt{3}})^{-2}$
$=(\sqrt[3]{3\sqrt{3}})^{-2}$
$(3\sqrt{3})^{\dfrac{-2}{3}} ....... (1)$
$3\sqrt{3}=3^{\dfrac{1}{2}+1}=3^{\dfrac{3}{2}} ....... (ii)$
Substituting $(ii)$ in $(i)$
$\left[(3)^{\dfrac{3}{2}}\right]^{\dfrac{-2}{3}}$
$=\dfrac{1}{3}=(3)^{-1}$