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

This entry was written by Nalin Pithwa, posted on September 22, 2020 at 2:57 am, filed under IITJEE Foundation mathematics. Bookmark the permalink. Follow any comments here with the RSS feed for this post. Post a comment or leave a trackback: Trackback URL.

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