Question

calcule as potências:

a) (√15)²

b) (3√7)²

c) (√7+√3)²

d) (3-√7)²​

Answer 1

Resposta:

a) 15

b) 63

c) 10 + 2√21

d) 16 - 6√7

Explicação passo-a-passo:

a) $\left(\sqrt{15}\right)^2=\left(15^{\frac{1}{2}}\right)^2=15^{\frac{1}{2}\cdot \:2}=15$

b) $\left(3\sqrt{7}\right)^2=3^2\left(\sqrt{7}\right)^2=9\left(\sqrt{7}\right)^2=9\cdot \:7=63$

c) $\left(\sqrt{7}+\sqrt{3}\right)^2=\left(\sqrt{7}\right)^2+2\sqrt{7}\sqrt{3}+\left(\sqrt{3}\right)^2=10+2\sqrt{21}$

d) $\left(3-\sqrt{7}\right)^2=3^2-2\cdot \:3\sqrt{7}+\left(\sqrt{7}\right)^2=16-6\sqrt{7}$