Hey y'all! Yesterday, we learned about squares, square roots, cubes, and cube roots. Here are the basics of all three: To start, here are some symbols and names relating to the unit. √ - This is a radical sign, which represents square roots. A radicand is the number inside the radical sign - √4 (It could be any number.) And the number to the left of the radical sign is the index - ∛ (An index can be any number, and indicates the number of identical factors needed to multiply to make the the number you're looking for.) Also note: any time a radical sign is present without an index, it means it has an index of 2, or more simply that it's a square root. (It takes too long to write out a two every time we have to write a square root.) To square a number is to multiply a number by itself twice. (Eg. 7² = 7 x 7 = 49, With 7² being the squared number.) It's called squaring because if you made a square with a surface area of 49 cm, each side would have 7 cm. A square root is a number that multiplies by itself to create a new number. For example, the square root of 81 is 9, because 9 x 9 = 81. √81 is also a way to symbolize a square root. Square roots don't even have to be rational. The square root of 6 is 2.4494897...etc. because that very long number times itself will still make 6. A perfect square is a number with a rational square root. (Eg. 6 x 6 = 36) Perfect squares can even be fractions, as long as the denominator and numerator separately are perfect squares. (Eg. 25/64 (I'm not sure how to do a fraction on here sorry) is a perfect square. 25 is a perfect square because 5 x 5 = 25 and 8 x 8 = 64.) To determine if a number is a perfect square without a calculator, simply start by finding all the prime factors of that number. (3 x 3 x 5 x 5 = 225) Then, distribute these four factors into two 'teams'. (3 x 5 vs. 3 x 5) If the factors can't be distributed equitably, then it's not a perfect square. Although, if the number is a perfect square, you can find the square root of that number by multiplying the numbers on each team together, and voila, that is the square root of the number. ( 3 x 5 = 15 and 15 x 15 = 225) Next up are cubes and cube roots. These are almost exactly the same as squares and square roots, but with the number 3 instead of 2. To cube a number is to multiply a number by itself three times. (Eg. 2 x 2 x 2 = 8) The cube root of a number is the factor of that number that multiplies itself by 3 to create that number. (The cube root of 8 is 2.) Again, cube roots do not have to be rational. We can identify a cube root by an index of 3 on the radical sign. (∛) Like square roots, there are perfect cubes which are numbers that have rational cube roots. (Eg. 4 x 4 x 4 = 64) Fractions can be perfect cubes as long as the numerator and denominator are perfect cubes individually. To find out if a number is a perfect cube without a calculator, find the prime factors of that number and almost exactly like with square roots, divide the factors into three even 'teams' and multiply them. (Remember: if the factors can't split evenly, it's not a perfect cube.) For example: 5 x 5 x 5 = 125. And there you have it, squares, square roots, cubes, and cube roots! Here's a video to summarize all of the above. (Side note: The way this guy draws his 2s is slightly disturbing.)
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Find your green dot!AuthorsWe are members of Esquimalt High School's Gifted Math 10 class. Most of us like Hi-Chews. Archives
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