Using a number line, what whole number and rational number to the nearest half is 58−−√ between?//
To find the whole number and rational number nearest to $\sqrt{58}$, we need to convert $\sqrt{58}$ into a mixed number by finding a whole number and a fraction equal to a value close to $\sqrt{58}$. We can start by finding whole numbers $a$ and $b$ such that $\sqrt{58}=a+\dfrac{b}{2}$. Let's square some numbers and look for one that is close to 58. \begin{align*}
4^2&=16 \\
6^2&=36 \\
7^2&=49 \\
8^2&=64
\end{align*} The square root of 64 is 8, which is too large because $4\leq\sqrt{58}<6$. Therefore, we conclude that $\sqrt{58}$ is between $a+\dfrac{0}{2}$ and $a+\dfrac{1}{2}$. The whole number nearest to $\sqrt{58}$ is $\boxed{7}$, which means $\sqrt{58}$ is between 7 and $\dfrac{1}{2}$.
Using a number line, what whole number and rational number to the nearest half is 58 square root between?
To find the whole number and rational number nearest to $\sqrt{58}$, we need to locate it on a number line and identify the closest whole number and the closest rational number to the nearest half.
First, we know that the square root of 58 is between 7 and 8 because $7^2 = 49$ and $8^2 = 64$, so $\sqrt{58}$ must be greater than 7 and less than 8.
Next, we divide the interval between 7 and 8 into halves:
$7\frac{1}{2}$
$7\frac{3}{2}$
Now, we can place $\sqrt{58}$ on the number line:
[asy]
unitsize(0.5cm);
for(int i = 5; i <= 9; ++i)
{
draw((-0.5,i)--(11.5,i));
label("$"+string(i)+"$", (-0.5,i), W);
}
draw((0,-1)--(0,10.5),EndArrow);
draw((11,0)--(-1,0),EndArrow);
label("$\sqrt{58}$", (7.6,8.5), N);
label("$7$",(7,0),S);
label("$7\frac{1}{2}$",(7.5,0),S);
label("$8$",(8,0),S);
[/asy]
Therefore, the whole number nearest to $\sqrt{58}$ is $\boxed{7}$, and the rational number nearest to the nearest half is $\boxed{7\frac{1}{2}}$.
Using a number line, what whole and rational number to the nearest half is 58 square root between?(1 point)
Responses
between 7 and 7.5
between 7 and 7.5
between 8.5 and 9
between 8.5 and 9
between 7.5 and 8
between 7.5 and 8
between 8 and 8.5
To find the whole number and rational number nearest to $\sqrt{58}$, we need to locate it on a number line and identify the closest whole number and the closest rational number to the nearest half.
First, we know that $\sqrt{58}$ is between $7$ and $8$ because $7^2 = 49$ and $8^2 = 64$, so $\sqrt{58}$ must be greater than $7$ and less than $8$.
Next, let's divide the interval between $7$ and $8$ into halves:
$7.5$
Now, we can place $\sqrt{58}$ on the number line:
[asy]
unitsize(0.5cm);
for(int i = 6; i <= 9; ++i)
{
draw((-0.5,i)--(11.5,i));
label("$"+string(i)+"$", (-0.5,i), W);
}
draw((0,5)--(0,10.5),EndArrow);
draw((11,5)--(-1,5),EndArrow);
label("$\sqrt{58}$", (7.6,8.5), N);
label("$7$",(7,5),S);
label("$7.5$",(7.5,5),S);
label("$8$",(8,5),S);
[/asy]
Therefore, the whole number nearest to $\sqrt{58}$ is $\boxed{7}$, and the rational number nearest to the nearest half is $\boxed{7.5}$.