#### Term 2 Real Numbers Five Marks Questions

9th Standard

Reg.No. :
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Maths

Time : 00:45:00 Hrs
Total Marks : 40
8 x 5 = 40
1. Find the 5th root of 32

2. Find the 5th root of 243.

3. Find the 5th root of 100000

4. Find the 5th root of $\frac{1024}{3125}$

5. Simplify the following using addition and subtraction properties of surds:
(i) 5$\sqrt{3}$ + 18$\sqrt{3}$-2$\sqrt{3}$
(ii) $4\sqrt [ 3 ]{ 5 } +2\sqrt [ 3 ]{ 5 } -3\sqrt [ 3 ]{ 5 }$
(iii) 3$\sqrt{75}$+5$\sqrt{48}$-$\sqrt{243}$
(iv) $5\sqrt [ 3 ]{ 40 } +2\sqrt [ 3 ]{ 625 } -3\sqrt [ 3 ]{ 320 }$

6. Simplify the following using multiplication and division properties of surds:
(i) $\sqrt { 3 } \times \sqrt { 5 } \times \sqrt { 2 }$
(ii) $\sqrt { 35 } \div \sqrt { 7 }$
(iii) $\sqrt [ 3 ]{ 27 } \times \sqrt [ 3 ]{ 8 } \times \sqrt [ 3 ]{ 125 }$
(iv) $(7\sqrt { a } -5\sqrt { b } )(7\sqrt { a } +5\sqrt { b } )$
(v) $\left[ \sqrt { \frac { 225 }{ 729 } } -\sqrt { \frac { 25 }{ 144 } } \right] \div \sqrt { \frac { 16 }{ 81 } }$

7. Arrange surds in descending order:
(i) $\sqrt [ 3 ]{ 5 } ,\sqrt [ 9 ]{ 4 } ,\sqrt [ 6 ]{ 3 }$
(ii) $\sqrt [ 2 ]{ \sqrt [ 3 ]{ 5 } } ,\sqrt [ 2 ]{ \sqrt [ 3 ]{ 5 } } ,\sqrt [ 3 ]{ \sqrt [ 4 ]{ 7 } } ,\sqrt { \sqrt { 3 } }$

8. Can you get a pure surd when you find
(i) the sum of two surds
(ii) the difference of two surds
(iii) the product of two surds
(iv) the quotient of two surds
Justify each answer with an example.