In the verge of coronavirus pandemic, we are providing FREE access to our entire Online Curriculum to ensure Learning Doesn't STOP!

Ex.1.5 Q2 Number System Solution - NCERT Maths Class 9

Go back to  'Ex.1.5'

Question

Simplify each of the following expressions

(i) $$(3 + \sqrt 3 )\,(2 + \sqrt 2 )$$

(ii) $$(3 + \sqrt 3 )\,(3 - \sqrt 3 )$$

(iii)$${(\sqrt 5 + \sqrt 2 )^2}$$

(iv) $$(5 - \sqrt 2 )\,(5 + \sqrt 2 )$$

Video Solution
Number Systems
Ex 1.5 | Question 2

Text Solution

Steps:

(i) \begin{align}(3 + \sqrt 3 )\,(2 + \sqrt 2 )\end{align}

By Distributive property

\begin{align}=6+3 \sqrt{2}+2 \sqrt{3}+\sqrt{6} \end{align}

(ii) \begin{align}(3 + \sqrt 3 )\,(3 - \sqrt 3 )\end{align}

Using the identity:

\begin{align}(a+b)(a-b) &=a^{2}-b^{2} \3+\sqrt{3}) 3-\sqrt{3} &=9-3 \\ &=6 \end{align} (iii) \(\begin{align}{(\sqrt 5 + \sqrt 2 )^2}\,\end{align}

Steps:

Using the identity: $$(a+b)^{2} =a^{2}+2 a b+b^{2}$$

\begin{align}&=(\sqrt{5})^{2}+2 \times \sqrt{5} \times \sqrt{2}+(\sqrt{2})^{2} \\ &=(5+2 \sqrt{10}+2) \\ &=7+2 \sqrt{10} \end{align}

(iv) \begin{align}(5 - \sqrt 2 )\,(5 + \sqrt 2 )\end{align}

Steps:

Using the identity: $$(a+b)(a-b) =a^{2}-b^{2}$$

\begin{align}&(\sqrt{5})^{2}-(\sqrt{2})^{2} \\ &=5-2 \\ &=3 \end{align}

Video Solution
Number Systems
Ex 1.5 | Question 2

Learn from the best math teachers and top your exams

• Live one on one classroom and doubt clearing
• Practice worksheets in and after class for conceptual clarity
• Personalized curriculum to keep up with school