Skill Check XV: IITJEE Maths: Foundation: Powers and Roots

Reference: An old ICSE text, class VIII, Oxford Publications, India: Abhijit Mukherjea et al.

Tutorial Exercises:

I) Evaluate \sqrt{38} - \sqrt[3]{38} (you may use a numerical log table)

II) Evaluate 2\sqrt{19} + 3 \sqrt[3]{15} (you may use a numerical log table).

III) Use your calculator to verify: 45^{3}-20^{3}=(45-20)(45^{2}+45 \times 20 +20^{2})

IV) Evaluate \sqrt[3]{980} correct up to three decimal places. You can use a log table.

V) Find the values of the following: use a log table in case you wish:

(5a) 23^{3} (5b) 49^{2} (5c) 28^{2} (5d) 39^{2} (5e) 47^{2} (5f) 19^{3} (5g) 27^{3} (5h) 36^{3} (5i) 41^{3} (5j) \sqrt{15} (5k) \sqrt{26} (5l) \sqrt{29} (5m) \sqrt{37} (5n) \sqrt{47} (5o) \sqrt[3]{13} (5p) \sqrt[3]{31} (5q) \sqrt[3]{22} (5r) \sqrt[3]{50} (5s) \sqrt[3]{34}

VI) Evaluate the following using log tables:

(6a) 19^{2}+10.5^{3} (6b) 45.1^{3}-30.9^{3} (6c) \sqrt{12}+\sqrt{15} (6d) \sqrt{27}-\sqrt{7} (6e) \sqrt[3]{43}+\sqrt[3]{34} (6f) \sqrt[3]{37}-\sqrt[3]{3} (6g) \sqrt{2}+\sqrt[3]{3}-\sqrt[3]{5} (6h) \sqrt[3]{49}+\sqrt[3]{50}-\sqrt{50} (6i) \sqrt{57} (6j) \sqrt{430} (6k) \sqrt[3]{99} (6l) \sqrt[3]{196}

Regards,

Nalin Pithwa

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