Maharashtra State Board Class 8 Maths Solutions Chapter 3 Indices and Cube Root Practice Set 3.1
Question 1.
Express the following numbers in index form.
i. Fifth root of 13
ii. Sixth root of 9
iii. Square root of 256
iv. Cube root of 17
v. Eighth root of 100
vi. Seventh root of 30
Solution:
i. \((13)^{\frac{1}{5}}\)
ii. \((9)^{\frac{1}{6}}\)
iii. \((256)^{\frac{1}{2}}\)
iv. \((17)^{\frac{1}{3}}\)
v. \((100)^{\frac{1}{8}}\)
vi. \((30)^{\frac{1}{7}}\)
Question 2.
Write in the form ‘nth root of a’ in each of the following numbers.
i. \((81)^{\frac{1}{4}}\)
ii. \((49)^{\frac{1}{2}}\)
iii. \((15)^{\frac{1}{5}}\)
iv. \((512)^{\frac{1}{9}}\)
v. \((100)^{\frac{1}{19}}\)
vi. \((6)^{\frac{1}{7}}\)
Solution:
i. Fourth root of 81.
ii. Square root of 49.
iii. Fifth root of 15.
iv. Ninth root of 512.
v. Nineteenth root of 100.
vi. Seventh root of 6.
Maharashtra Board Class 8 Maths Chapter 3 Indices and Cube Root Practice Set 3.1 Intext Questions and Activities
Question 1.
Using laws of indices, write proper numbers in the following boxes. (Textbook pg, no. 14)
i. \({ 3 }^{ 5 }\times { 3 }^{ 2 }={ 3 }^{ \left( \right) }\)
ii. \({ 3 }^{ 7 }\div { 3 }^{ 9 }={ 3 }^{ \left( \right) }\)
iii. \(({ 3 }^{ 4 })^{ 5 }={ 3 }^{ \left( \right) }\)
iv. \(5^{ -3 }=\frac { 1 }{ { 5 }^{ \left( \right) } }\)
v. \(5^{ 0 }=\left( \right) \)
vi. \(5^{ 1 }=\left( \right) \)
vii. \((5\times 7)^{ 2 }={ 5 }^{ \left( \right) }\times { 7 }^{ \left( \right) }\)
viii. \({ \left( \frac { 5 }{ 7 } \right) }^{ 3 }=\frac { { \left( \right) }^{ 3 } }{ { \left( \right) }^{ 3 } } \)
ix. \({ \left( \frac { 5 }{ 7 } \right) }^{ -3 }={ \left( \frac { \left( \right) }{ \left( \right) } \right) }^{ 3 }\)
Solution:
i. \({ 3 }^{ 5 }\times { 3 }^{ 2 }={ 3 }^{ 7 }\)
ii. \({ 3 }^{ 7 }\div { 3 }^{ 9 }={ 3 }^{ -2 }\)
iii. \(({ 3 }^{ 4 })^{ 5 }={ 3 }^{ 20 }\)
iv. \(5^{ -3 }=\frac { 1 }{ { 5 }^{ 3 } } \)
v. \(5^{ 0 }=1\)
vi. \(5^{ 1 }=5\)
vii. \((5\times 7)^{ 2 }={ 5 }^{ 2 }\times { 7 }^{ 2 }\)
viii. \({ \left( \frac { 5 }{ 7 } \right) }^{ 3 }=\frac { { 5 }^{ 3 } }{ { 7 }^{ 3 } } \)
ix. \({ \left( \frac { 5 }{ 7 } \right) }^{ -3 }={ \left( \frac { 7 }{ 5 } \right) }^{ 3 }\)