7 answers
To find the product of \( 5\sqrt{16} \) and \( 3\sqrt{5} \), let's start by simplifying each term:
Simplify \( \sqrt{16} \): \[ \sqrt{16} = 4 \] Thus, \[ 5\sqrt{16} = 5 \times 4 = 20 \]
The second term \( 3\sqrt{5} \) is already in simplest form.
Now, let's multiply the two simplified terms:
\[ 20 \times 3\sqrt{5} = 60\sqrt{5} \]
Thus, the product of \( 5\sqrt{16} \) and \( 3\sqrt{5} \) in simplest form is:
\[ \boxed{60\sqrt{5}} \]
To find the product of 5√16 and 3√5, we start by simplifying each term.
First, simplify √16: √16 = 4 So, 5√16 = 5 × 4 = 20.
Next, the second term 3√5 is already in simplest form.
Now, multiply the two simplified terms: 20 × 3√5 = 60√5.
Thus, the product of 5√16 and 3√5 in simplest form is 60√5.
The statement provided is not entirely correct.
Rational Number: A rational number is any number that can be expressed as the ratio of two integers, such as \( \frac{a}{b} \) where \( a \) and \( b \) are integers and \( b \neq 0 \).
Irrational Number: An irrational number cannot be expressed as the ratio of two integers and its decimal expansion does not terminate or repeat.
The product we found, \( 60\sqrt{5} \), is in fact an irrational number because \( \sqrt{5} \) is irrational. The decimal expansion of \( \sqrt{5} \) does not terminate or repeat, and multiplying it by 60 does not change its irrational nature.
Thus, the conclusion is:
Actually, that statement is incorrect in regard to the product \( 60\sqrt{5} \).
To clarify:
Rational Number: A number is rational if it can be expressed as the ratio of two integers (for example, \(\frac{a}{b}\), where \(a\) and \(b\) are integers, and \(b \neq 0\)). Rational numbers have decimal expansions that either terminate (like 0.5, which is \(\frac{1}{2}\)) or eventually repeat (like 0.333..., which is \(\frac{1}{3}\)).
Irrational Number: A number is irrational if it cannot be expressed as a ratio of two integers. Its decimal expansion does not terminate and does not repeat. For instance, \(\sqrt{2}\) and \(\sqrt{5}\) are irrational numbers.
Since \( \sqrt{5} \) is irrational, \( 60\sqrt{5} \) is also irrational. Therefore, it cannot be expressed as a ratio of two integers. Its decimal expansion is non-terminating and non-repeating.
In conclusion, \( 60\sqrt{5} \) is not rational; it is irrational. The correct understanding is that it cannot be written as the ratio of two integers.
