How do you simplify radical expressions? There are two common ways to simplify radical expressions, depending on the denominator. Using the identities #\sqrt {a}^2=a# and # (a-b) (a+b)=a^2-b^2#, in fact, you can get rid of the roots at the denominator. Case 1: the denominator consists of a single root. For example, let's say that our fraction ...
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Simplifying #sqrt20# by prime factorisation:. #sqrt20 = sqrt(2^2 *5)=color(blue)(2sqrt5# The expression can now be written as
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The first few terms are: 0,1,4,17,72,305,1292,5473. The ratio between terms will tend to 2 + √5. So we find: √5 ≈ 5473 1292 − 2 = 2889 1292 ≈ 2.236068. Answer link. The square root of 5 can't be simplified father than it already is, so here is sqrt5 to ten decimal places: sqrt5~~2.2360679775...
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No: sqrt(5)+sqrt(5) = 2sqrt(5) = sqrt(4)sqrt(5) = sqrt(20) ~~ 4.472135955 sqrt(10) = sqrt(2*5) = sqrt(2)sqrt(5) ~~ 3.16227766 In the above answer, I use sqrt(ab) = sqrt(a)sqrt(b) - which is true for any a, b >= 0. Generalisation Suppose f is a function that takes any Real number and gives us another Real number. Under what circumstances would we expect the following: f(a+b) = f(a) + f(b) for ...
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See explanation... Here's a sketch of a proof by contradiction: Suppose sqrt(5) = p/q for some positive integers p and q. Without loss of generality, we may suppose that p, q are the smallest such numbers. Then by definition: 5 = (p/q)^2 = p^2/q^2 Multiply both ends by q^2 to get: 5 q^2 = p^2 So p^2 is divisible by 5. Then since 5 is prime, p must be divisible by 5 too. So p = 5m for some ...
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Explanation: square root of 5 to the 3rd power can be written as. (√5)3. = √5 ⋅ √5 ⋅ √5. We know that √a ⋅ √a = a. Hence √5 ⋅ √5 ⋅ √5 = 5√5. √5 ≈ 2.236.
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The square root is expressed as an exponent of 1/2, so sqrt(x^5) can be expressed as x^(5/2). Roots are expressed as fractional exponents: root(2)x=x^(1/2) root(3)x=x^(1/3) and so on. This makes sense, because when we multiply we add exponents: sqrt(x) x sqrt(x) = x x^(1/2) x x^(1/2) = x^((1/2+1/2)) = x^1 = x When an exponent is raised to another exponent, the exponents are multiplied: sqrt(x ...
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To find the square root of 225 using these prime numbers, take one number from each set of two and multiply them together: {eq}5\cdot3=15 {/eq}. 15 is the square root of 225.
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5 when you square and square root a number they cancel out. 5^2 =25 sqrt(25) = 5. Algebra . Science ...
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So how many times do we multiply 5 by to get 5? Answer: once. Therefore: #5=5^1# Now let's talk about the square root. If we take #sqrt5# and multiply by itself twice, we get: #sqrt5xxsqrt5=5# Remember that when we are multiplying numbers with exponents and the same base, the rule is: #x^axxx^b=x^(a+b)# and so we can see that #sqrt5=5^(1/2)#:
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