Question

Evaluate 0.8 correct upto two decimal .

Answer 1

Answer is 0.89

Hope it helps.

Answer 2

Answer:

0.89

Step-by-step explanation:

0.8

=0.89

Step-by-step explanation:

Given : Number \sqrt{0.8}

Complete step-by-step answer:

Let us take $x = \sqrt {0.8} $.

We shall square on both sides to get ${x^2} = 0.8$.

We can write $0.8{\text{ as }}\dfrac{8}{{10}}$ because there is only one digit after the decimal in 0.8.

Thus, we have ${x^2} = \dfrac{8}{{10}}$

Now, we will multiply and divide by 10 on the LHS i.e., ${x^2} = \dfrac{8}{{10}} \times \dfrac{{10}}{{10}} = \dfrac{{80}}{{100}}$ ………………(1)

We will now prime factorise the numerator i.e., 80 and express it as a square. Thus,

$80 = 8 \times 10$

$ \Rightarrow 80 = 2 \times 2 \times 2 \times 2 \times 5$

Rewriting the multiples as exponent, we get

$ \Rightarrow 80 = {2^2} \times {2^2} \times 5 \\

\Rightarrow 80 = {(2 \times 2 \times \sqrt 5 )^2} = {(4\sqrt 5 )^2} \\ $

Also, we know that the denominator i.e., $100 = {10^2}$. Substituting these values in equation (1), we get

${x^2} = \dfrac{{{{(4\sqrt 5 )}^2}}}{{{{(10)}^2}}}$ ………………………..(2)

Now, we will take square root on both sides of equation (2). Hence,

$\Rightarrow$ $x = \dfrac{{4\sqrt 5 }}{{10}}$

We know that $\sqrt 5 = 2.236$.

Multiplying this value by 4 in the numerator, we get

$\Rightarrow$ $x = \dfrac{{4 \times 2.236}}{{10}} = \dfrac{{8.944}}{{10}}$.

Dividing $8.944{\text{ by }}10$, we get $x = 0.8944$.

Since we have to evaluate $\sqrt {0.8} $ up to two decimal places, we finally get $\sqrt {0.8} = 0.89$.