Answer:
[tex]\frac{\sqrt{24}- \sqrt{54} }{\sqrt{6}}[/tex] = -1
[tex]\sqrt{\frac{9}{20}[/tex]*[tex]\frac{10\sqrt{2} }{3\sqrt{5} }[/tex] = 1.4142
[tex]\frac{10\pi\sqrt{2}-8\pi\sqrt{2}}{2\sqrt{2}}[/tex] = π =3.14159
[tex]\pi\sqrt{\frac{5}{3}}\cdot\pi\sqrt{\frac{3}{5}}[/tex] = π² = 9.8696
Explanation:
1.) Rewrite √24 = [tex]\sqrt{4*6} = 2\sqrt{6}[/tex] Rewrite √54 =[tex]\sqrt{9*6}= 3\sqrt{6}[/tex]
Divide both terms by the denominator; √6 cancels. 2-3 = -1
2.) Rewrite as [tex]\frac{3}{2\sqrt{5}}[/tex] ×[tex]\frac{10\sqrt{2}}{3\sqrt{5}}[/tex] The 3's cancel. 10/2 = 5√2 in the numerator.
√5 × √5 = 5 in the denominator. The 5's cancel.
That leaves √2 ≈1.4142
3.) Divide the terms in the numerator by the term in the denominator.
√2's cancel. 10π/2 = 5π 8π/2 = 4π
Subtract and we are left with π = 3.14159
4.) [tex]\pi\sqrt{\frac{5}{3}}\cdot\pi\sqrt{\frac{3}{5}}[/tex] The square roots are reciprocals. They multiply to 1
We are left with π × π = π² ≈ 9.8696
