(6) The value of [tex]\sqrt{64}[/tex] is 8.
(7) The value of [tex]-\sqrt{31}[/tex] is -5.6
(8) The value of [tex]-\sqrt{16}[/tex] is -4
Explanation:
(6) The expression is [tex]\sqrt{64}[/tex]
Since, 64 is a perfect square, this can be written as [tex]8 \times 8[/tex].
Thus, the expression can be written as
[tex]\sqrt{64}=\sqrt{8 \times 8}=\sqrt{8^{2} }[/tex]
The square root gets cancelled. Thus, we have,
[tex]\sqrt{64}=8[/tex]
Thus, the value of [tex]\sqrt{64}[/tex] is 8.
(7) The expression is [tex]-\sqrt{31}[/tex]
Since, 31 is not a perfect square and solving the expression using a calculator, we get,
[tex]-\sqrt{31}=-5.56776[/tex]
Rounding off to the nearest tenth, we get,
[tex]-\sqrt{31}=-5.6[/tex]
Thus, the value of [tex]-\sqrt{31}[/tex] is -5.6
(8) The expression is [tex]-\sqrt{16}[/tex]
Since, 16 is a perfect square, this can be written as [tex]4\times 4[/tex]
Thus, the expression can be written as
[tex]-\sqrt{16}=-\sqrt{4\times 4}=-\sqrt{4^{2} }[/tex]
The square root gets cancelled. Thus, we have,
[tex]-\sqrt{16}=-4[/tex]
Thus, the value of [tex]-\sqrt{16}[/tex] is -4.
