Jump to

- Chapter 1- Rational and Irrational Numbers
- Chapter 2- Compound Interest [Without Using Formula
- Chapter 3- Compound Interest [Using Formula
- Chapter 4- Expansions
- Chapter 5- Factorisation
- Chapter 6- Simultaneous Equations
- Chapter 7- Indices [exponents]
- Chapter 8- Logarithms
- Chapter 9- Triangles [Congruency in Triangles]
- Chapter 10- Isosceles Triangle
- Chapter 11- Inequalities
- Chapter 12- Mid-Point and Its Converse
- Chapter 13- Pythagoras Theorem
- Chapter 14- Rectilinear Figures
- Chapter 15- Construction of Polygons
- Chapter 16- Area Theorems
- Chapter 17- Circles
- Chapter 18- Statistics
- Chapter 19- Mean and Median
- Chapter 20- Area and Perimeter of Plane Figures
- Chapter 21- Solids
- Chapter 22- Trigonometrical Ratios
- Chapter 23- Trigonometrical Ratios of Standard Angles
- Chapter 24- Solution Of Right Triangles
- Chapter 25- Complementary angles
- Chapter 26- Co-ordinate Geometry
- Chapter 27- Graphical Solution
- Chapter 28- Distance Formula

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}

"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"

Related Questions

Was This helpful?

Chapters

Lido

Courses

Quick Links

Terms & Policies

Terms & Policies

2022 © Quality Tutorials Pvt Ltd All rights reserved