Many mental calculations are easier the more facts you memorize. Knowing the squares up to $31^2=961$ can make it easier, reducing the need to go all the way to single digits. Also the fact that $(10n+5)^2=100n(n+1)+25$, for example $65^2=(6\cdot7)25=4225$. If you break it all the way to individual digits, I find it easier to keep track of my place if I start with the most significant digits and add as I go, so $359^2=300^2+2\cdot300\cdot50+\ldots =90000+10000+\ldots$$359^2=300^2+2\cdot300\cdot50+\ldots =90000+30000+\ldots$ $=100000+ 50^2+\ldots = 102500+2\cdot300\cdot9+\ldots=107900+2\cdot50\cdot9+9^2$$=120000+ 50^2+\ldots = 122500+2\cdot300\cdot9+\ldots=127900+2\cdot50\cdot9+9^2$ where for many purposes you can quit early when you have the precision needed.
Many mental calculations are easier the more facts you memorize. Knowing the squares up to $31^2=961$ can make it easier, reducing the need to go all the way to single digits. Also the fact that $(10n+5)^2=100n(n+1)+25$, for example $65^2=(6\cdot7)25=4225$. If you break it all the way to individual digits, I find it easier to keep track of my place if I start with the most significant digits and add as I go, so $359^2=300^2+2\cdot300\cdot50+\ldots =90000+10000+\ldots$ $=100000+ 50^2+\ldots = 102500+2\cdot300\cdot9+\ldots=107900+2\cdot50\cdot9+9^2$ where for many purposes you can quit early when you have the precision needed.
Many mental calculations are easier the more facts you memorize. Knowing the squares up to $31^2=961$ can make it easier, reducing the need to go all the way to single digits. Also the fact that $(10n+5)^2=100n(n+1)+25$, for example $65^2=(6\cdot7)25=4225$. If you break it all the way to individual digits, I find it easier to keep track of my place if I start with the most significant digits and add as I go, so $359^2=300^2+2\cdot300\cdot50+\ldots =90000+30000+\ldots$ $=120000+ 50^2+\ldots = 122500+2\cdot300\cdot9+\ldots=127900+2\cdot50\cdot9+9^2$ where for many purposes you can quit early when you have the precision needed.
Many mental calculations are easier the more facts you memorize. Knowing the squares up to $31^2=961$ can make it easier, reducing the need to go all the way to single digits. Also the fact that $(10n+5)^2=100n(n+1)+25$, for example $65^2=(6*7)25=4225$$65^2=(6\cdot7)25=4225$. If you break it all the way to individual digits, I find it easier to keep track of my place if I start with the most significant digits and add as I go, so $359^2=300^2+2*300*50+\ldots =90000+10000+\ldots$$359^2=300^2+2\cdot300\cdot50+\ldots =90000+10000+\ldots$ $=100000+ 50^2+\ldots = 102500+2*300*9+\ldots=107900+2*50*9+9^2$$=100000+ 50^2+\ldots = 102500+2\cdot300\cdot9+\ldots=107900+2\cdot50\cdot9+9^2$ where for many purposes you can quit early when you have the precision needed.
Many mental calculations are easier the more facts you memorize. Knowing the squares up to $31^2=961$ can make it easier, reducing the need to go all the way to single digits. Also the fact that $(10n+5)^2=100n(n+1)+25$, for example $65^2=(6*7)25=4225$. If you break it all the way to individual digits, I find it easier to keep track of my place if I start with the most significant digits and add as I go, so $359^2=300^2+2*300*50+\ldots =90000+10000+\ldots$ $=100000+ 50^2+\ldots = 102500+2*300*9+\ldots=107900+2*50*9+9^2$ where for many purposes you can quit early when you have the precision needed.
Many mental calculations are easier the more facts you memorize. Knowing the squares up to $31^2=961$ can make it easier, reducing the need to go all the way to single digits. Also the fact that $(10n+5)^2=100n(n+1)+25$, for example $65^2=(6\cdot7)25=4225$. If you break it all the way to individual digits, I find it easier to keep track of my place if I start with the most significant digits and add as I go, so $359^2=300^2+2\cdot300\cdot50+\ldots =90000+10000+\ldots$ $=100000+ 50^2+\ldots = 102500+2\cdot300\cdot9+\ldots=107900+2\cdot50\cdot9+9^2$ where for many purposes you can quit early when you have the precision needed.
Many mental calculations are easier the more facts you memorize. Knowing the squares up to $31^2=961$ can make it easier, reducing the need to go all the way to single digits. Also the fact that $(10n+5)^2=100n(n+1)+25$, for example $65^2=(6*7)25=4225$. If you break it all the way to individual digits, I find it easier to keep track of my place if I start with the most significant digits and add as I go, so $359^2=300^2+2*300*50+\ldots =90000+10000+\ldots$ $=100000+ 50^2+\ldots = 102500+2*300*9+\ldots=107900+2*50*9+9^2$ where for many purposes you can quit early when you have the precision needed.