its just dificult
whats the square root of 49x and x has a exponent of 6
As a rule you should know that square roots can be multiplied and divided into each other, but they can not be added or subtracted from each other.
Means that √a . √b = √ab , i.e. √9 . √4 = √36 = 6
√32 . √2 2 =3 * 2 = 6
This means that multiplying 2 square roots we get product as square root with argument as product of each factor, like example above.
We also know by the basic definition roots and exponent are opposite of each other.
n√xn = x
We use these property to simplify square roots with big magnitude.
√X2n =(√X2) n = Xn
√X2n+1 = √X2n . √X = Xn . √x
The last 2 statements gives a rule for simplifying any square roots with argument
as power of a factor to even number, i,e. √X 2n , or odd number as √X2n+1 .
Juniper...let me add a small element you should know, when it comes to solving problems with a coefficient and a variable(I'm assuming you know what these terms are...). Rule/Skill 1: when solving the power of an expression(finding the square...cubed...root...etc) of an expression...separate the expression into the constants(values you know) and the variables(values you don't know), in your case. /49x^6 basically the square root of the expression 49 x to the 6th power. This is the same as 49 times x to the 6th power and can be written like this /(49) x /(x^6) in this case...I'm using / to represent square root. I'm sure you already know, the square root of 49 is /49 = 7, that's for the knowns. Now, for the unknowns /x^6 which in words is the square root of x to the 6th power. So (some value x) times (some value x) equals x^6. As it turns out, as explained above (x^3) times (x^3) equals x^6 or (x^3)(x^3) = x^6. Finally; /49x^6 = 7x^3 Hope that helps...good luck
In real domain,
sqrt(49x^6) = 7|x^3|
Attn: 7x^3 is incorrect since in real domain sqrt(49x^6) is larger than or equal to 0 even if x < 0.
When you enter a question, there is an option in the icon menu to create an exponent... the one marked x2.
You can write 49 x^6 or 49x6. The latter might be better since it looks just like what you're seeing in a textbook.
The symbol ^ is called a hat and it is used to indicate an exponent....such as in your question is would look like "What is the square root of 49x^6.....the answer is 7x^3....depending on your teacher the x^3 should be in absolute value symbols because you took the even root of an even exponent and its result was an odd exponent.