HiSET: Math : Properties of operations with real numbers
Study concepts, example questions & explanations for HiSET: Math
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Example Questions
Example Question #4 : Irrational Numbers
Simplify the difference:
None of the other choices gives the correct response.
To simplify a radical expression, first find the prime factorization of the radicand. First, we will simplify 
By the Product of Radicals Property,
11 is a prime number, so 
Through substitution, and the distribution property:
Example Question #11 : Irrational Numbers
Simplify:
The expression is already simplified.
To simplify a radical expression, first find the prime factorization of the radicand, which is 40 here.
Pair up like factors, then apply the Product of Radicals Property:
the simplest form of the radical.
Example Question #28 : Numbers And Operations On Numbers
Simplify the sum:
The expression cannot be simplified further.
The expression cannot be simplified further.
To simplify a radical expression, first find the prime factorization of the radicand. First, we will attempt simplify 
Since no prime factor appears twice, the expression cannot be simplified further. The same holds for 
It follows that the expression 
Example Question #12 : Irrational Numbers
Consider the expression 
To simplify this expression, it is necessary to first multiply the numerator and the denominator by:
When simplifying a fraction with a denominator which is the sum or difference of an integer and a square root, it is necessary to first rationalize the denominator. This is accomplished by multiplying both halves of the fraction by the conjugate of the denominator—the result of changing the plus symbol to a minus symbol (or vice versa); therefore, both halves of the given expression must be multiplied by the conjugate of 
Example Question #13 : Irrational Numbers
Multiply:
The two expressions comprise the sum and the difference of the same two expressions, and can be multiplied using the difference of squares formula:
The square of the square root of an expression is the expression itself, so:
Example Question #14 : Irrational Numbers
Simplify:
The expression is already simplified.
To simplify a radical expression, first find the prime factorization of the radicand, which is 120 here.
Pair up like factors, then apply the Product of Radicals Property:
the simplest form of the radical.
Example Question #32 : Hi Set: High School Equivalency Test: Math
Simplify the difference:
The expression cannot be simplified further.
The expression cannot be simplified further.
To simplify a radical expression, first, find the prime factorization of the radicand. First, we will attempt simplify 
Since no prime factor appears twice, the expression cannot be simplified further. The same holds for 
It follows that the expression 
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