Babajaro
Radici, potenze, numeri reali
<h3>4. Pretvorp u decimap:</h3>
<p>
<p>$\frac{2}{5}$</p>
<p>$2\frac{2}{5}$</p>
<p>$3\frac{1}{4}$</p>
<p>$\frac{6}{100}$</p>
<p>$\frac{9}{10}$</p>
<p>$\frac{1836}{1000}$</p>
</p>
<h3>5. Sedi izrazi:</h3>
<p>
<p>$4\sqrt{10} - 7\sqrt{10} = $</p>
<p>$4\sqrt{10} \cdot 7\sqrt{10} = $</p>
<p>$(4\sqrt{10})^2 = $</p>
<p>$5\sqrt{2} \cdot 4\sqrt{8} = $</p>
<p>$\sqrt{3} \cdot \sqrt{6} = $</p>
<p>$(3\sqrt{7} - 2\sqrt{5}) \cdot (\sqrt{5} - \sqrt{7}) = $</p>
<p>$(3\sqrt{3} - 2\sqrt{2}) \cdot (3\sqrt{3} + 2\sqrt{2}) = $</p>
<p>$\left(\frac{4\sqrt{3}}{\sqrt{2}}\right)^2 = $</p>
<p>$(2\sqrt{3} - 3\sqrt{5})^2 = $</p>
<p>$\sqrt{18} - 3\sqrt{8} = $</p>
<p>$\frac{4}{2\sqrt{5}} = $</p>
<p>$\frac{3}{5-\sqrt{2}} = $</p>
<p>$\frac{\sqrt{2}}{\sqrt{3}-1} = $</p>
</p>
<h3>6. Sedi izrazi:</h3>
<p>
<p>$\sqrt{144} - \sqrt{25-9} = $</p>
<p>$\frac{\sqrt{49} - \sqrt{81}}{7} - \frac{(\sqrt{5})^2}{\sqrt{225}} = $</p>
<p>$\left(\frac{2\sqrt{5} - 2\sqrt{3}}{3\sqrt{7}}\right)^2 = $</p>
<p>$(\sqrt{3} + 2)^2 - (5\sqrt{3})^2 - 5\sqrt{3} = $</p>
<p>$(2 - 3\sqrt{2})^2 - (5 - 2\sqrt{2})^2 = $</p>
<p>$(2\sqrt{3})^2 - (2 - \sqrt{12})^2 - \sqrt{3} = $</p>
<p>$5\sqrt{3} \cdot 2\sqrt{8} - \sqrt{3} \cdot 4\sqrt{3} - 2\sqrt{2} \cdot 5\sqrt{12} - 4\sqrt{2} \cdot 3\sqrt{2} - \sqrt{3} \cdot \sqrt{2} = $</p>
</p>
<h2>Choose correct answer(s) from the given choices</h2>
<p>
<strong>(1)</strong> The sum of two numbers is 129, and their difference is 11. Find the numbers.
</p>
<p>
 a. 71 and 60 <br>
 b. 71 and 59 <br>
 c. 70 and 60 <br>
 d. 70 and 59
</p>
<p>
<strong>(2)</strong> Draw the graph of the equation \(-3x - y = -3\). At what points does the graph cut the \(x\)-axis and \(y\)-axis?
</p>
<p>
 a. \(x\)-axis at \(A(1, 0)\) and \(y\)-axis at \(B(0, 3)\) <br>
 b. \(x\)-axis at \(A(7, -3)\) and \(y\)-axis at \(B(-2, 8)\) <br>
 c. \(x\)-axis at \(A(4, 1)\) and \(y\)-axis at \(B(2, 5)\) <br>
 d. \(x\)-axis at \(A(3, 0)\) and \(y\)-axis at \(B(0, 4)\)
</p>
<p>
<strong>(3)</strong> Divide \(30\sqrt{30}\) by \(5\sqrt{6}\).
</p>
<p>
 a. \(6\sqrt{8}\) <br>
 b. \(9\sqrt{6}\) <br>
 c. \(6\sqrt{5}\) <br>
 d. \(5\sqrt{6}\)
</p>
<p>
<strong>(4)</strong> The sum of Jamie's age and half of Joe's age is 30. Also, one-third of Jamie's age added to twice Joe's age is 36. Find the sum of their ages.
</p>
<p>
 a. 30 years <br>
 b. 36 years <br>
 c. 38 years <br>
 d. 52 years
</p>
<p>
<strong>(6)</strong> \(\sqrt{5}\) is a _________ number.
</p>
<p>
 a. whole <br>
 b. rational <br>
 c. natural <br>
 d. irrational
</p>
<h2>Answer the questions</h2>
<p>
<strong>(7)</strong> Trains A and B leave the station at the same time. Train A travels in the south direction, and train B travels in the west direction. Train A is 20 km/hour slower than train B. After 5 hours, trains are 500 km apart. Find the speed of both trains.
</p>
<p>
<strong>(8)</strong> Read the statements carefully. <br>
<em>Statement I:</em> The quadratic equation \(ax^2 + bx + c = 0\) has two distinct real roots if \(b^2 - 4ac > 0\). <br>
<em>Statement II:</em> The quadratic equation \(2(a^2 + b^2)x^2 + 2(a + b)x + 1 = 0\) has no real roots when \(a \neq b\). <br>
Which of the above statements is true?
</p>
<p>
<strong>(9)</strong> Find the arithmetic mean between \(h+g\) and \(h-g\).
</p>
<p>
<strong>(10)</strong> The number \(x = 4.181818...\) is expressed in the form \(\frac{p}{q}\), where \(p\) and \(q\) are positive integers having no common factors. Find the value of \(p-q\).
</p>