Zad. 1
[tex]a = \sqrt{81-\sqrt{289}} = \sqrt{81-17} =\sqrt{64} =8[/tex]
Odp. c
Zad. 2
[tex]\sqrt{48}-2 \sqrt{27} +\sqrt{12} =\sqrt{16 \cdot 3}-2 \sqrt{9 \cdot 3} +\sqrt{4 \cdot 3} =4\sqrt{3}-6 \sqrt{3} +2\sqrt{3} =0[/tex]
Zad. 3
a)
[tex]\sqrt[4]{2} \cdot \sqrt[4]{8} = \sqrt[4]{2 \cdot 8} =\sqrt[4]{16} = \sqrt[4]{2^4} =2[/tex]
b)
[tex]\sqrt[3]{250} : \sqrt[3]{2} =\sqrt[3]{250:2} =\sqrt[3]{125} =\sqrt[3]{5^3} =5[/tex]
c)
[tex](\sqrt[5]{30})^5 = 30[/tex]
d)
[tex]\sqrt{\sqrt{81}} =\sqrt{9} = 3[/tex]
e)
[tex]\sqrt{\sqrt[3]{7}} : \sqrt[6]{7} = (7^{\frac{1}{3}})^{\frac{1}{2}} : 7^{\frac{1}{6}}=7^{\frac{1}{3} \cdot \frac{1}{2}} : 7^{\frac{1}{6}}=7^{\frac{1}{6}} : 7^{\frac{1}{6}} = 1[/tex]
f)
[tex]5 \cdot (\sqrt{\sqrt[3]{5^2}})^3 = 5 \cdot 5^{\not{2}^1 \cdot \frac{1}{\not{3}_1} \cdot \frac{1}{\not{2}_1} \cdot \not{3}^1} = 5 \cdot 5^1 = 5 \cdot 5=25[/tex]
