Question

6. Calculează:
a) V(-7)² =
b) (V3)⁵× V3 =
c) (V75)³:(V3)³=​

Answer 1

$a)\sqrt{( - 7) {}^{2} } = \sqrt{7 {}^{2} } = 7 \\ b)\sqrt{ {3}^{5} } \times \sqrt{3} = \sqrt{3 {}^{6} } = \\ = \sqrt{3 {}^{2} \times {3}^{2} \times {3}^{2} } = 3 \times 3 \times 3 = 27$

$c) \sqrt{75} {}^{3} \div \sqrt{3} {}^{3} = \\ = 75 \sqrt{75} \div 3 \sqrt{3} = 75 \div 3 \sqrt{75 \div 3} = \\ = 25 \sqrt{25} = 25 \times 5 = 125$

Answer 2

$\it a)\ \sqrt{(-7)^2}=\sqrt{49}=7\\ \\ b)\ (\sqrt3)^5\cdot\sqrt3=(\sqrt3)^{5+1}=(\sqrt3)^6=[(\sqrt3)^2]^3=3^3=27\\ \\ \\ c)\ \ (\sqrt{75})^3:(\sqrt3)^3=\Big(\dfrac{\sqrt{75}}{\sqrt3}\Big)^3=\Big(\sqrt{\dfrac{75}{3}}\Big)^3=(\sqrt{25})^3=5^3=125$