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Units Digits in Cube Numbers

Write true T ...

Question

Write true $(T)$ or false $(F)$ for the following statements:
If $a^{2}$ ends in $9,$ then $a^{3}$ ends in $7$

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Solution

Step: State true or false

Given statement: If $a^{2}$ ends in $9,$ then $a^{3}$ ends in $7$

Consider the value: $a = 7$
$\Rightarrow a^{2} = 7 \times 7 = 49,$ which ends in $9$

Now,
$a^{3} = 7 \times 7 \times 7 = 343,$ which ends in $3$

Therefore, if $a^{2}$ ends in $9,$ then $a^{3}$ does not always ends in $7.$

Hence, the given statement is false.

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Similar questions

Q. Write true (T) or false (F) for the following 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, a³ is always greater than a².
(vi) If a and b are integers such that a² > b², then a³ > b³.
(vii) If a divides b, then a³ divides b³.
(viii) If a²ends in 9, then a³ ends in 7.
(ix) If a² ends in 5, then a³ ends in 25.
(x) If a² ends in an even number of zeros, then a³ ends in an odd number of zeros.

Question 71

State whether the following statement is true or false:

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

(T)

(F)

for the following statements:
If

a

b

are integers such that

a^{2} > b^{2},

a^{3} > b^{3}

(T)

(F)

for the following statements:
If

a^{2}

ends in an even number of zeros, then

a^{3}

ends in an odd number of zeros.

(T)

(F)

for the following statements:
If

a

b,

a^{3}

b^{3}

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Units Digits in Cube Numbers

Standard VIII Mathematics

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