Question

can some one explain how to work them out please

Answer 1

25.\[\frac{ 4\sqrt{150} }{ ? \sqrt{189x}}\]

Answer 2

\(\bf \color{blue}{189\implies 3\cdot 3\cdot 3\cdot 7\implies 3^2\cdot 3\cdot 7
\\ \quad \\
150\implies 2\cdot 3\cdot 5\cdot 5\implies 2\cdot 3\cdot 5^2}\\ \quad \\ \quad \\

\cfrac{ 4\sqrt{150} }{ \sqrt{189x}}\implies \cfrac{4\sqrt{{\color{blue}{ 2\cdot 3\cdot 5^2}}}}{\sqrt{{\color{blue}{ 3^2\cdot 3\cdot 7}}}\cdot x}\)

Answer 3

ok @jdoe0001 can you explain one more

Answer 4

ok

Answer 5

\[\frac{ 4\sqrt{6} }{ \sqrt{30} }\]

Answer 6

@jdoe0001

Answer 7

27. \[(2\sqrt{5}+3\sqrt{7})^{2}\]

Answer 8

you'd do the same, you factor the radicands and see what you can take out and cancel like terms

Answer 9

\(\bf \cfrac{ 4\sqrt{6} }{ \sqrt{30} }\implies \cfrac{ 4\sqrt{2\cdot 3} }{ \sqrt{2\cdot 3\cdot 5} }\implies \cfrac{ 4\cancel{\sqrt{2\cdot 3}} }{ \cancel{\sqrt{2\cdot 3}}\cdot \sqrt{5} }\)

Answer 10

\(\bf (2\sqrt{5}+3\sqrt{7})^2\implies (2\sqrt{5})^2+(3\sqrt{7})^2\implies 2^2\sqrt{5^2}+3^2\sqrt{7^2}\)

Answer 11

@deshawn1