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How do you simplify multiplying square roots with variables?

Factor the radicandsFactor the radicands of the square roots to prime numbers, and write out the powers of the variables. For the equation 2 * sqrt(4 * x^5 * y) * sqrt(9 * x^3 * y), the factored out version is 2 * sqrt(2 * 2 * x * x * x * x * x * y) * sqrt(3 * 3 * x * x * x * y).Group any like terms togetherIn the factored square roots, group any two like terms together and bring them outside of the square root as a single term. The equation 2 * sqrt(2 * 2 * x * x * x * x * x * y) * sqrt(3 * 3 * x * x * x * y) becomes 2 * 2 * x * x * sqrt(xy) * 3 * x * sqrt(xy).Multiply out the factored equat..

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What fractions are less than 1 over 2?

In order to compare the size of fractions, they must have a common denominator. With a common denominator, the fraction with a smaller numerator is smaller. As an example, 1/2 and 2/9 could be re-written as 9/18 and 4/18 respectively. It is clear that 4/18, or 2/9 is the smaller of the pair.

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How is the volume of an ellipsoid calculated?

An ellipsoid is a three-dimensional version of an ellipse in the same manner as a sphere is a three-dimensional version of a circle. It is uncertain when the concept of an ellipse was discovered, though it is believed that the ancient Greeks knew around 350 B.C. that slicing a section of a cone by a two-dimensional plane at an angle, rather than parallel to its base, would produce the conic geometric shape known as an ellipse.Rather than being a perfect sphere, the Earth is an ellipsoid. Isaac Newton and other British scientists were the first to theorize that the Earth was an ellipsoid. Measu..

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What are the properties of a cube?

The volume of a cube that has edges of length "x" is x times x times x, which can also be written as x cubed or x^3. The surface area of the same cube is 6 times x times x, or 6 x^2. A cube can also be called a regular hexahedron.

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What is a contradiction equation?

One example of a contradiction equation would be x+5 = x+2. No possible constant value for x exists to make this a true equation. There is no way to add 5 and 2 to the same number and end up with the same result. Attempting to solve this sort of reaction ends up with a clear contradiction. In this example, subtracting x from both sides yields 5=2.

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How do you calculate a weighted average?

Determine the data valuesDetermine the value of each data in the set. These are referred to as "x" in the formula.\nFind the product of w and xMultiply each data value, x, by its weight, w. \nCalculate the weighted averageUsing the formula for finding a weighted average, find the sum of all the products of the numbers and their respective weights. This is the weighted average. \n

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What is one percent of one billion?

Percentage is a ratio expressed as a fraction with 100 in the denominator. Fifty percent is the same as 50/100, which reduces to 1/2. In more complex calculations, percent value is found by finding the ratio and then multiplying by 100. For example, to find the percentage that 50 out of 1250 represents, divide 50 by 1250, which equals 0.04, then multiply by 100, so 50 is 4 percent of 1250.

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What is geodesic dome math?

A geodesic line joins two points on a sphere with the shortest possible distance between them; and a geodesic dome is created from a lattice of geodesic lines that intersect to cover the curved surface with triangles. The more triangles there are, the more complex the network, and hence the more closely the dome approximates the actual shape of a sphere. Each member of the structure contributes equally to the whole. This makes geodesic domes lightweight yet strong, self-bracing structures that use very little material and are ideal for construction.\nA geodesic dome is constructed from multipl..

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What is an example of perpendicular lines in real life?

Other real-world examples of perpendicular lines include graph paper, plaid patterns on fabric, square lines of floor tiles, lines of mortar on brick walls, the intersecting lines of a Christian cross, metal rods on the cooking surface of a barbecue grill, wooden beams in the wall of a house, and the designs on country flags such as Norway, the United Kingdom, Switzerland, Greece, Denmark and Finland. Perpendicular lines form the corner of squares and rectangles in various real-world shapes.\nPerpendicular lines create four right angles at their intersection point, making 360 degrees total. Pe..

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What is the hypotenuse angle theorem?

This theorem is valid for right triangles, or triangles in which there is a 90-degree angle. In a right triangle, the hypotenuse is the longest side or leg of the triangle. The hypotenuse also is opposite the 90-degree angle.\nLikewise, the Pythagorean Theorem relates the three sides of a right triangle. In a right triangle where side “c” is the hypotenuse length and “b” and “an” are the two other side lengths, this theorem states that the hypotenuse length squared is equal to the sum of the each side length squared.\nBesides using an acute angle and the hypotenuse of a right trian..

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