If $a^{2}$ ends in $9,$ then $a^{3}$ will end in:

7

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3

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5

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none of the above

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Solution

The correct options are
A $7$
B $3$
Given that, $a^{2}$ ends in $9$ .
To find out: What will $a^{3}$ end in?

$a^{2}$ ends in $9$
$∴ a$ will either end in $3$ or $7$ .

Case I: If $a$ ends in $3$ :
$∴ a^{3}$ will end in $7 [∵ 3 \times 3 \times 3 = 2 7 -]$ .

Case II: If $a$ ends in $7$ :
$∴ a^{3}$ will end in $3 [∵ 7 \times 7 \times 7 = 34 3 -]$ .

Hence, both A and B are correct.

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Q. If

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Question 71

State whether the following statement is true or false:

If $a^{2}$ ends in 9, then $a^{3}$ ends in 7.

Question 71

State whether the following statement is true or false:

If $a^{2}$ ends in 9, then $a^{3}$ ends in 7.

Write true (T)I or false (f) for the followiong statements:
(i) 392 is a perfect cube.
(ii) 8640 is not a perfect cube.
(iii) No cube can end with exactly two zeros.
(iv) There is no perfect cube which ends in 4.
(v) For an integer $a, a^{3}$ is always greater than $a^{2}$
(vi) if a and b are integers such that $a^{2} > b^{2}, t h e n a^{3} > b^{3}$
(vii) If a adivides b, then $a^{3}$ divides $b^{3}$
(viii) If $a^{2}$ ends in 9 then $a^{3}$ ends in 7.
(ix) If $a^{2}$ ends in 5, then $a^{3}$ ends in 25.
(x) If $a^{2}$ ends in an even number of zeros. than $a^{3}$ ends in an odd number of zeros.

Question 70

State whether the following statement is true or false:

If $a^{2}$ ends in 5, then $a^{3}$ ends in 25.

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If a2 ends in 9, then a3 will end in:

The correct options are A 7 B 3Given that, a2 ends in 9.To find out: What will a3 end in?a2 ends in 9∴ a will either end in 3 or 7.Case I: If a ends in 3:∴ a3 will end in 7[∵ 3×3×3=27–].Case II: If a ends in 7:∴ a3 will end in 3[∵ 7×7×7=343–].Hence, both A and B are correct.

If $a^{2}$ ends in $9,$ then $a^{3}$ will end in: