Selina Solutions Class 9 Mathematics Solutions for Exercise 1(B) in Chapter 1 - Chapter 1- Rational and Irrational Numbers

Question 2 Exercise 1(B)

Find the square of:

$\begin{aligned} &\text { (i) }\\ &\left(\frac{3 \sqrt{5}}{5}\right)^{2} \end{aligned}$

$\begin{aligned} &\text { (ii) }\\ &\sqrt{3}+\sqrt{2} \end{aligned}$

$\begin{aligned} &\text { (iii) }\\ &\sqrt{5}-2 \end{aligned}$

$\text { (iv) } \quad 3+2 \sqrt{5}$

Answer:

(i) $\begin{aligned} \left(\frac{3 \sqrt{5}}{5}\right)^{2} &=\frac{3^{2}(\sqrt{5})^{2}}{5^{2}} \\ &=\frac{9 \times 5}{25} \\ &=\frac{9}{5} \\ &=1 \frac{4}{5} \end{aligned}$

(ii) $\begin{aligned} (\sqrt{3}+\sqrt{2})^{2}=&(\sqrt{3})^{2}+2(\sqrt{3})(\sqrt{2})+(\sqrt{2})^{2} \\ &=3+2 \sqrt{6}+2=5+2 \sqrt{6} \end{aligned}$

(iii) $\begin{aligned} (\sqrt{5}-2)^{2} &=(\sqrt{5})^{2}-2(\sqrt{5})(2)+(2)^{2} \\ &=5-4 \sqrt{5}+4 \\ &=9-4 \sqrt{5} \end{aligned}$

(iv) $\begin{aligned} (3+2 \sqrt{5})^{2} &=3^{2}+2(3)(2 \sqrt{5})+(2 \sqrt{5})^{2} \\ &=9+12 \sqrt{5}+20 \\ &=29+12 \sqrt{5} \end{aligned}$

Video transcript

"hello everyone welcome to leader learning so we are going to solve the question on the screen so we have to find the squares of these four numbers so these are irrational numbers and we have to find the squares so let us take up the first question which says 3 under root 5 divide by 5 and we have to find the whole square so this will result into 3 whole square into root 5 whole square and the denominator is 5 whole square which will be equal to 9 into 5 divided by 25 so this will give us 9 by 5 which is the answer to the first part coming up to the second part so root 3 plus root 2 whole square so we will use the identity a plus b whole square so this will give us a square plus b whole square plus 2 times of a b so 2 times of root 2 into root 3 this will give us 3 plus 2 plus 2 under root 6 which gives us the answer as 5 plus 2 under root 6. now coming up to the third part so under root 5 minus 2 whole square is what we have to find so similar to the second part we'll do as under root 5 whole square minus 2 into 2 is 4 under root 5 plus 2 whole square which is 4 so this gives us 5 minus 4 root 5 plus 4 which is equal to 9 minus 4 under root 5 which is the answer to the third part now coming up to the last part which is the fourth part so fourth part says 3 plus 2 under root 5 whole square is equal to now a square is 3 whole square plus b square is 2 whole square into under root 5 whole square plus twice of a b so twice into 3 into b which is 2 root 5 so which finally comes out as 9 plus 4 into 5 is 20 plus 3 to the 6 into 12 under root 5 which finally comes out to be as 29 plus 12 under root 5 which is the answer to the fourth part so this is how we will solve so friends if you have any concerns please write down below the video and subscribe to the channel thank you"

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